Question

How to find the y-intercept of the line $y = x + 2$ ?

Answer 1

Hint : We can solve this in two methods. The first method Is comparing the given equation with the slope intercept form equation so we can get the y-intercept. The second method is using the definition of y-intercept. The point where a line or curve crosses the y-axis of a graph. In other words finding the value of y at ‘x’ equal to zero.

Complete step-by-step answer :
Given, $y = x + 2$ .
Let’s see the method 1:
We know the equation of slope-intercept form is $y = mx + b$ , where ‘m’ is slope and ‘b’ is the y-intercept.
Comparing with the given equation we will have, slope is 1 and y-intercept is 2.
Hence, my intercept is 2.
Let’s see method 2:
We have $y = x + 2$ .
By the definition of y-intercept. To find the y-intercept we need to put the value of ‘x’ equal to zero, that is $x = 0$ .
$\Rightarrow y = 0 + 2$
$\Rightarrow y = 2$
Thus, we have y-intercept is 2.
So, the correct answer is “2”.

Note : Here the given equation is in standard form in comparison with the slope intercept form. If not then we need to simplify the given equation. In both methods we get the same answer. We can also find the x-intercept for the given problem. The point where a line or curve crosses the x-axis of a graph is called x-intercept. In other words finding the value of x at ‘y’ is equal to zero. Let’s put $y = 0$ in $y = x + 2$ .
$\Rightarrow 0 = x + 2$
$\Rightarrow x = - 2$ . That is -2 is the x-intercept.