Question

How do you find the intercepts for 2x-y = -4?

Answer 1

Hint: In this question, we are given an equation and we need to find its intercept which means we need to find the points where these points cut the x-axis and y-axis. For finding the x-intercept (the point where the line cuts the x-axis) we will put y = 0 and find the value of x. Our point will be (x,0) for finding y-intercept (the point where the line cuts y-axis) we will put x = 0 and solve for y. Our point will be (0,y).

Complete step by step answer:
Here we are given the equation of a line as 2x-y = -4.
We need to find the intercept of this line. For this let us first understand the meaning of intercept.
The point where the line or curve crosses the axis of the graph is called an intercept. If a point crosses the x axis, then it is called an x-intercept. If a point crosses the y axis then it is called the y-intercept. For finding the x-intercept, we need to put the value of y as 0 and solve for x whereas for finding the y-intercept, we need to put the value of x as 0 and solve for y.
Here the equation is 2x-y = -4.
For finding the x-intercept let us put the value of y as 0 we get, $2x-0=-4\Rightarrow 2x=-4$ .
Dividing both sides by 2 we get, ${\displaystyle \frac{2x}{2}}={\displaystyle \frac{-4}{2}}\Rightarrow x=-2$ .
Therefore, the x-intercept is -2. The point will be of the form (x,0). So here the point of x-intercept is (-2,0).
For finding the y intercept let us put the value of x as 0 we get $2\left(0\right)-y=-4\Rightarrow -y=-4$ .
Canceling negative signs from both sides we get, y = 4.
Therefore, the intercept is 4. The point will be of the form (0,y). So here the point of y-intercept is (0,4). Hence our required intercept are (-2,0) and (0,4)
With the help of these intercept, our graph will look like this,

Note:
 Students should take care of the signs while calculating intercept. Note that, for an equation of the form ${\displaystyle \frac{x}{a}}+{\displaystyle \frac{y}{b}}=1$ intercept are given by (a,0) and (0,b). So we can also convert the equation into this form and find the intercept. Given equation is 2x-y = -4. Dividing both sides by -4, we get ${\displaystyle \frac{2x-y}{-4}}={\displaystyle \frac{-y}{4}}\Rightarrow {\displaystyle \frac{2x}{-4}}-{\displaystyle \frac{y}{-4}}=1$ .
Simplifying we get ${\displaystyle \frac{x}{-2}}+{\displaystyle \frac{y}{4}}=1$ .
Which is of the form ${\displaystyle \frac{x}{a}}+{\displaystyle \frac{y}{b}}=1$ where a = -2 and b = 4.
So, the required intercepts are (-2,0) and (0,4) which are the same as found earlier.