Question

How do you graph $y=\dfrac{1}{4}x-5$?

Answer 1

In this problem, we have to graph the given equation. To graph the equation, we have to find the x-intercept and the y-intercept. We know that at the x-intercept, the value of y is 0 and at y-intercept, the value of x is 0. By substituting x equal to 0, we can get the y-intercept and y equal to 0, we can get x-intercept and we can plot the points in the graph.

Complete step-by-step solution:
We know that the given equation is,
$y=\dfrac{1}{4}x-5$……. (1)
Now we can find the x-intercept.
We know that at x-intercept, the value of y is 0.
We can substitute for y = 0, in equation (1), we get

& \Rightarrow 0=\dfrac{1}{4}x-5 \\\ & \Rightarrow \dfrac{1}{4}x=5 \\\ \end{aligned}$$ Now we can multiply by 4 on both sides and cancel similar terms, we get $$\begin{aligned} & \Rightarrow \dfrac{4x}{4}=5\times 4 \\\ & \Rightarrow x=20 \\\ \end{aligned}$$ The x-intercept is $$\left( 20,0 \right)$$ Now we can find y-intercept. We know that at y-intercept, the value of x is 0. We can substitute for x = 0, in equation (1), we get $$\begin{aligned} & \Rightarrow y=\dfrac{1}{4}\left( 0 \right)-5 \\\ & \Rightarrow y=-5 \\\ \end{aligned}$$ The y-intercept is $$\left( 0,-5 \right)$$ . We can also find other points, through which the line passes. For y = -2, the value of x is $$\begin{aligned} & \Rightarrow -2=\dfrac{x}{4}-5 \\\ & \Rightarrow \dfrac{x}{4}=3 \\\ & \Rightarrow x=12 \\\ \end{aligned}$$ Therefore, the x-intercept is $$\left( 20,0 \right)$$, the y-intercept is $$\left( 0,-5 \right)$$ and the other point is $$\left( 12,-2 \right)$$ Now, we can plot the graph using the x-intercept $$\left( 20,0 \right)$$, the y-intercept $$\left( 0,-5 \right)$$and the other point $$\left( 12,-2 \right)$$.  **Note:** Students make mistakes while finding the value for x-intercept and the y-intercept, we should know that at the x-intercept, the value of y is 0 and at y-intercept, the value of x is 0. By substituting x equal to 0, we can get the y-intercept and y equal to 0, we can get x-intercept and we can plot the points in the graph.