Question

How do you use the intercept to graph $-x+4y=8$?

Answer 1

Hint: In this question, we are given an equation of line and we need to draw the graph of that line using the intercepts. So we will first find the intercepts (x intercept and y intercept) and then use them to plot the graph. The x intercept is the point found by putting y = 0 in the equation of line. The y intercept is the point found by putting x = 0 in the equation of line. We will plot these points on the line and then draw a line passing through them which will be the required line.

Complete step-by-step answer:
Here we are given the equation of line as $-x+4y=8$. We need to find the intercept of this line such that we can plot a graph for this equation of line. As we know, the y intercept is the point where the line crosses the y axis i.e. when x = 0 and x intercept is the point where the line crosses the x axis i.e. when y = 0. So let us find these intercepts.
For y intercept let us put the value of x as 0 in the equation of line $-x+4y=8$ we get 4y = 8.
Dividing both sides by 8 we get $\dfrac{4y}{4}=\dfrac{8}{4}$.
Simplifying we get y = 2.
So the point where the line cuts the y axis is (0,2).
For x intercept let us put the value of y as 0 in the equation of line $-x+4y=8$ we get $-x+0=8\Rightarrow -x=8\Rightarrow x=-8$.
So the point where the line cuts the x axis is (-8,0).
Hence the two points lying on the line are given by (0,2) and (-8,0).
Let us plot these points on the graph and join the line passing through them. This line is the required equation of the line $-x+4y=8$. The graph looks like this,

Note: Students should take care of the signs of coordinate while plotting the graph. For finding the intercept students can also convert the given equation of line in the form $\dfrac{x}{a}+\dfrac{y}{b}=1$ where a and b will be x and y intercepts respectively. Here we have the equation of line as $-x+4y=8$. Dividing both sides by 8 we get $\dfrac{-x}{8}+\dfrac{4y}{8}=\dfrac{8}{8}$.
Simplifying we get $\dfrac{x}{-8}+\dfrac{y}{2}=1$.
This equation is of the form $\dfrac{x}{a}+\dfrac{y}{b}=1$. So, -8 will be the x intercept and 2 will be the y intercept which are the same as obtained earlier.