Question

How do you find the slope and intercept to graph $y=\dfrac{1}{2}(x-4)$?

Answer 1

The standard linear equation is y = mx + c. This is called the slope-intercept form. Our problem will also be solved with this formula. First, we will find the slope, then the y-intercept, and then the x-intercept. So let’s see how we can solve our problem.

Complete step by step solution:
We have to find the slope and intercept form of $y=\dfrac{1}{2}(x-4)$. Here, we will use the standard form of a linear equation which is y = mx + c. In the linear equation y = mx + c, m is the slope. For our problem $\dfrac{1}{2}$ will be the slope as it is the coefficient of x.
To find out y-intercept, we will substitute 0 for x
$\Rightarrow y=\dfrac{1}{2}.0-4$
$\Rightarrow y=-4$
Therefore, the y-intercept is -4.
To find out x-intercept, we will substitute 0 for y
$\Rightarrow 0=\dfrac{1}{2}x-4$
$\Rightarrow \dfrac{1}{2}x=4$
$\Rightarrow x=8$
Therefore, the x-intercept is 8.

Hence, the slope is $\dfrac{1}{2}$ , the y-intercept is -4 and x-intercept is 8 for the line $y=\dfrac{1}{2}(x-4)$.

Note:
In the above problem while finding y-intercept we substituted 0 for x because on the y-axis the value of x is 0. And the same goes for the x-intercept, on the x-axis the value of y is 0. Also, the standard linear form is important because based on that we find the slope of the line.