Question

How do you find the slope and intercept to graph $y=5x-9$?

Answer 1

In this given problem, we have a line equation, in which we have to find the slope and intercepts, to plot the graph. We know that slope intercept form is $y=mx+c$ where m is the slope and c is the y-intercept. By using the slope intercept formula, we can find the slope. We also know that for x-intercept the value of y is 0 and for y-intercept the value of x is 0. From these points, we can plot the graph.

Complete step by step answer:
We know that the given slope intercept form is,
$y=5x-9$ ……… (1)
We also know that the general form of the slope intercept form is,
$y=mx+c$ ……… (2)
Where, m is the slope and c, y-intercept.
Now we can compare equation (1) and (2), we get
Slope, m = 5 and y-intercept, c = -9
We also know that at y-intercept, x = 0.
Therefore, the point at y-intercept is $\left( 0,-9 \right)$.
Now, we have to find the x-intercept.
We know that at x-intercept, y = 0. Substituting the value of y in equation (1), we get

& \Rightarrow 0=5x-9 \\\ & \Rightarrow x=\dfrac{9}{5}=1.8 \\\ \end{aligned}$$ Therefore, the point at x-intercept is $$\left( 1.8,0 \right)$$. We can also find some other points to be plotted in the graph where the line passes through. We can assume for x = 1, then from (1). $$\begin{aligned} & \Rightarrow y=5\left( 1 \right)-9 \\\ & \Rightarrow y=-4 \\\ \end{aligned}$$ Therefore, the other point is $$\left( 1,-4 \right)$$. Now we can plot the graph using x-intercept $$\left( 1.8,0 \right)$$, y-intercept $$\left( 0,-9 \right)$$ and the other point $$\left( 1,-4 \right)$$.  **Note:** Students make mistakes in finding the value of x-intercept and y-intercept, we should know that at x-intercept the value of y is 0 and at y-intercept the value of x is 0. We should also concentrate on formulae like slope intercept formulas, to solve these types of problems.