Horizontal And Vertical Lines Algebra 1 Homework Answers
Carlita Giandomenico
In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on railway tracks, etc.
Horizontal means "side-to-side" hence horizontal line is a sleeping line, whereas, vertical means "up-to-down" therefore a vertical line is a standing line. Horizontal lines are lines drawn from left to right or right to left and are parallel to the x-axis. Vertical lines are lines drawn up and down and are parallel to the y-axis. Vertical & horizontal lines are perpendicular to each other.
Horizontal lines are lines that are parallel to the ground (or horizon). In coordinate geometry, horizontal lines are lines that are parallel to the x-axis and form the equation, y = b, where 'b' is constant. As there is no change in the y-coordinate the slope of a horizontal line is equal to zero.
A horizontal line is a line that is parallel to the x-axis of the coordinate plane and its equation is of the form y = b, where 'b' is constant, whereas, a vertical line is a line parallel to the y-axis and its equation is of the form x = b, where 'b' is constant.
A horizontal line is drawn side to side, parallel to the x-axis of a coordinate plane and it is perpendicular to the y-axis. The up and down line is a vertical line and it is parallel to the y-axis and perpendicular to the x-axis.
Horizontal lines and vertical lines both adhere to linear equations. The typical equation of a straight line is eqy=mx+b /eq. Here, m is the slope and b is the y-intercept. The slope is given by the slope formula from above:
Now, given the equation of either a horizontal or vertical line, it is possible to find its slope. If the equation is of a horizontal line, which means it it has the form eqy=c /eq, the slope is therefore zero. By choosing any two distinct points on the line, the slop equation will always be eq\frac0x_2-x_1=0 /eq.
Now, given the graph of a horizontal or vertical line, is it possible to determine its equation? Simply put, the answer is yes. Given any graph of a horizontal line or a vertical line, identify the corresponding y-value or x-value which leads to the equations being eqy=c /eq or eqx=d /eq respectively (for c, d real numbers). This is to say that once the type of graph and the y-value or x-value is known, then the equation is also known. Here are some examples:
Furthermore, given the equation of a horizontal line or a vertical line, it is possible to graph said line on a coordinate grid. To graph a horizontal or vertical line, simply find a point that lies on the line, eq(0, c) \textor (c, 0) /eq for horizontal lines and vertical lines respectively. Then, plot either a horizontal line or a vertical line depending on the equation. Finally, it is also possible to find the equation of a horizontal or vertical line given its graph. Firstly, identify if the graph is of a horizontal line or a vertical line; this will give the equation form. Then, find a point that lies on the graph and record its x-value or y-value. Then, the equation is known: eqy=c \textor x=d /eq for c and d real numbers. Here are the important parts of this lesson:
All right, let's take a moment to review what we've learned. Linear equations in general are functions that graph to form a straight line and are typically written as y = mx + b, where m is the slope and b is the y-intercept. Horizontal lines go left and right and are in the form of y = b, where b represents the y-intercept, while vertical lines go up and down and are in the form of x = a where a represents the shared x-coordinate of all points. All you need to do is remember these.
The slope of a horizontal line is always zero and the slope of a vertical line is always undefined. Simply identify if the equation or graph is that of a horizontal or vertical line and then the slope is known.
To find horizontal or vertical lines given an equation, simply locate a point that lies on the line and then draw either a horizontal line or vertical line through said point. Or, if the graph is known, identify if it is of a horizontal or vertical line. Then locate the x-value or y-value that lies on the line. Finally, create the equation using this information.
In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate. For example, (2,0), (3,0) (-4,0), etc. are the points of vertical lines. Similarly, the line which goes from left to right and is parallel to the x-axis is called a horizontal line.
When we graph lines, we typically begin with a point and then use the slope to determine the line. There are, however, some special exceptions. These are called horizontal and vertical lines.
We can still graph them with ease once we understand what they are and how they work! Continue on to learn more including the slope of a horizontal line, the slope of a vertical line, and what these special lines look like.
A contour line is a line drawn on a topographic map to indicate ground elevation or depression. A contour interval is the vertical distance or difference in elevation between contour lines. Index contours are bold or thicker lines that appear at every fifth contour line.
If the numbers associated with specific contour lines are increasing, the elevation of the terrain is also increasing. If the numbers associated with the contour lines are decreasing, there is a decrease in elevation. As a contour approaches a stream, canyon, or drainage area, the contour lines turn upstream. They then cross the stream and turn back along the opposite bank of the stream forming a "v". A rounded contour indicates a flatter or wider drainage or spur. Contour lines tend to enclose the smallest areas on ridge tops, which are often narrow or very limited in spatial extent. Sharp contour points indicate pointed ridges.
Example 1 - In the graphic below, what is the vertical distance between the contour lines?
Pick two contour lines that are next to each other and find the difference in associated numbers.
40 feet - 20 feet = 20 feet
The contour lines in this figure are equally spaced. The even spacing indicates the hill has a uniform slope. From the contour map, a profile can be drawn of the terrain.
Example 2 - Draw a profile showing the elevations of the contours.
Note: The intervals are increasing, therefore, the contours indicate a hill. The peak is normally considered to be located at half the interval distance.
Widely separated contour lines indicate a gentle slope. Contour lines that are very close together indicate a steep slope.
The figure above illustrates various topographic features. (b) Notice how a mountain saddle, a ridge, a stream, a steep area, and a flat area are shown with contour lines.
The figure above illustrates a depression and its representation using contour lines. Notice the tick marks pointing toward lower elevation.
I been trying few formulas and google search, but wasn't able to find anything that would help my problem. To keep it simple, as explained in the attached picture, how do I drag down formula vertically, while continue the horizontal cell reference in the formula
If you want to drag both horizontally and vertically to populate the whole table in this fashion, the first cell would be =$A2-B$1. As you move horizontally, the only thing that will change is the column B reference. Moving vertically, the only thing that will change is the row 2 reference.
Three minutes is three units to the right on the horizontal axis, Time. If you lightly draw a vertical line up from 3, the point where the vertical line intersects the graph is the answer. Put a dot at this point and read the temperature on the vertical axis. The temperature of the gas at three minutes is approximately 35 degrees Celsius.
- The graph below highlights the 5 definitions:
- The x axis is the horizontal axis, and x is the independent variable.
- The scale of the x axis is 5.
- The y axis is the vertical axis, and y is the dependent variable.
- The scale of the y axis is 25.
- The ordered pair is indicated by (x, y).
- The x intercepts are approximately (-2.5, 0) and (27.5, 0).
- The y intercept is approximately (0, 75).
This section presents an additional way to graph a line. To graph a line, you need a minimum of two points. Two special points can be used. They are the intercepts of each axis. Often the intercepts have special meanings in a mathematical model. Also covered in this section are horizontal and vertical lines.
You should write the equations for horizontal and vertical lines on a note card. You will need to graph horizontal lines in the Section 2.9 Applications of Graphs. You should review this card at least twice a week.
Explanation: 34.55 - 28.15, represents the change in cost. Cost is the dependent variable and the vertical axis.
30-10, represents the change in miles. Miles are the independent variable and the horizontal axis.
The basic ideas in this section:
- The formula for the slope of a line is .
- If the slope of a line is positive, then the line is increasing or rising from left to right.
- If the slope of a line is negative, then the line is decreasing or falling from left to right.
- The slope of a horizontal line is zero.
- The slope of a vertical line is undefined.
- In the slope-intercept equation, y = mx + b, m is the slope, and (0,b) is the y intercept.