Explanation:
- Calculate the slope with two given coordinate points by using rise over run.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let these points
[tex] \begin{cases}(x_1, y_1) = ( - 4, - 1) \\ (x_2, y_2) = ( 2, 8) \end{cases}[/tex]
[tex]m = \frac{8 - ( - 1)}{2 - ( - 4)} \\ m = \frac{8 + 1}{2 + 4} \Longrightarrow \frac{9}{6} \Longrightarrow \frac{3}{2} \\ m = \frac{3}{2} [/tex]
[tex]y = mx + b \\ m = slope \\ b = y - intercept[/tex]
Substitute the value of m in the equation.
[tex]y = \frac{3}{2} x + b[/tex]
- Substitute any coordinate points that are given or part of the graph in the equation.
[tex](x_, y) = ( - 4, - 1)[/tex]
[tex] - 1 = \frac{3}{2} ( - 4) + b[/tex]
- Solve the equation for b-term.
[tex] - 1 = \frac{3}{ \cancel{2}} ( \cancel{ - 4}) + b\\ - 1 = 3( - 2) + b \\ - 1 = - 6 + b \\ - 1 + 6 = b \\ 5 = b[/tex]
- Rewrite the equation by substituting the value of b in the equation.
[tex]y = \frac{3}{2} x + 5[/tex]
Answer
[tex] \large \boxed{y = \frac{3}{2} x + 5}[/tex]
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