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Question: How do you graph the lines using the slope-intercept form \(h\left( x \right)=-x+7?\)...

How do you graph the lines using the slope-intercept form h(x)=−x+7?h\left( x \right)=-x+7?

Explanation

Solution

We are required to plot the given equation in the slope intercept form on the graph. From the given slope intercept form, we find out the slope and the y-intercept. Then we plot the y-intercept value on the y-axis at which x is 0. Then we find out the slope to obtain the relation between x and y and how they vary with respect to each other. We then vary them and plot another point and we obtain the graph of this line by joining these 2 points.

Complete step-by-step solution:
To solve this question, we need to consider the equation in the slope-intercept form. The slope intercept form is given by y=mx+c.y=mx+c. Here, m is the slope of the given line and c is the y-intercept.
The given equation is already in slope intercept form,
⇒h(x)=−x+7\Rightarrow h\left( x \right)=-x+7
Here, comparing the two equations, we can see that the y-intercept is 7. This means that the line intersects the y-axis at a point 7 units from the origin. We plot this point on the graph as (0,7).\left( 0,7 \right).
We can also see that the slope is -1. This can be represented as
⇒m=change in y directionchange in x direction=−1\Rightarrow m=\dfrac{\text{change in y direction}}{\text{change in x direction}}=-1
⇒change in y direction=−change in x direction\Rightarrow \text{change in y direction}=-\text{change in x direction}
This shows that the change in x direction is opposite in direction but equal in magnitude for a change in the y direction. Let us assume from the point (0,7),\left( 0,7 \right), y increases by 1 unit and moves up by 1 unit. This indicates that x decreases by 1 unit indicating the new point to be at (−1,8).\left( -1,8 \right). Plotting this point too and joining the two points, we obtain the graph of this line as shown in the figure below.

Hence, we have graphed the line using the slope-intercept form for h(x)=−x+7.h\left( x \right)=-x+7.

Note: It is important to know the standard slope intercept form to solve this problem. We can also solve this question by substituting the value for the points of x-coordinates and obtaining the values for the y-coordinates. We then plot 2 such points on the graph and join them and obtain the line for this equation.