Question

Write the equation of the line passing through the points (-4,-1) and (2,8)

Answer 1

Step-by-step explanation:

• Calculate the slope with two given coordinate points by using rise over run.

`m = (y_2 - y_1)/(x_2 - x_1)`

Let these points

`\begin{cases}(x_1, y_1) = ( - 4, - 1) \\ (x_2, y_2) = ( 2, 8) \end{cases}`

`m = (8 - ( - 1))/(2 - ( - 4)) \\ m = (8 + 1)/(2 + 4) \Longrightarrow (9)/(6) \Longrightarrow (3)/(2) \\ m = (3)/(2)`

• Slope-Intercept

`y = mx + b \\ m = slope \\ b = y - intercept`

Substitute the value of m in the equation.

`y = (3)/(2) x + b`

• Substitute any coordinate points that are given or part of the graph in the equation.

`(x_, y) = ( - 4, - 1)`

`- 1 = (3)/(2) ( - 4) + b`

• Solve the equation for b-term.

`- 1 = \frac{3}{ \cancel{2}} ( \cancel{ - 4}) + b\\ - 1 = 3( - 2) + b \\ - 1 = - 6 + b \\ - 1 + 6 = b \\ 5 = b`

• Rewrite the equation by substituting the value of b in the equation.

`y = (3)/(2) x + 5`

Answer

`\large \boxed{y = (3)/(2) x + 5}`

If you have any questions related to the answer, feel free to ask via comment.