Explanation
[tex]y = mx + b \\ m = slope \\ b = y - intercept[/tex]
- Calculate the slope with two given coordinate by using rise over run.
[tex] \begin{cases}(x_1,y_1) = ( - 4,0) \\ (x_2,y_2) = ( 0,2) \end{cases}[/tex]
These two coordinate points are part of the graph and can be used to find the slope.
[tex]m = \frac{y_2 -y_1 }{x_2 - x_1} [/tex]
Substitute the coordinate points in the formula.
[tex]m = \frac{2 - 0}{0 - ( - 4)} \\ m = \frac{2}{ 4} \\ m = \frac{1}{2} [/tex]
Therefore, the slope is 2.
Rewrite the equation in slope-intercept.
[tex]y = \frac{1}{2} x + b[/tex]
- Calculate the y-intercept by substituting any given points in new rewritten equation.
[tex](x,y) = ( 0,2)[/tex]
I will be substituting these coordinate points in the equation.
[tex]y = \frac{1}{2} x + b[/tex]
Substitute x = 0 and y = 5 in the equation.
[tex]2 = \frac{1}{2} (0) + b \\ 2 = 0 + b \\ 2 = b[/tex]
Therefore the y-intercept is (0,2).
Rewrite the equation.
[tex]y = \frac{1}{2} x + 2[/tex]
Answer
[tex] \large \boxed{y = \frac{1}{2} x + 2}[/tex]
If you have any questions related to the answer, feel free to ask me via comment.
