Question

A line passes through the points (-4, -16) and (0, 12). What is its equation in slope-intercept

form?

Answer 1

`\large \boxed{y = 7x + 12}`

Explanation:

Goal

• Write the equation of a line in slope-intercept form.

Given

• Coordinate points which are (0,12) and (-4,-16).

Step 1

• Find the slope by using slope formula or rise over run which is the changes of y over the changes of x

`\large{m = (y_2-y_1)/(x_2-x_1)}`

Substitute the coordinate points in the formula.

`m = (12 - ( - 16))/(0 - ( - 4)) \\ m = (12 + 16)/(0 + 4) \\ m = (28)/(4) \longrightarrow (7)/(1) \\ m = 7`

Step 2

• Rewrite the equation by substituting the slope in slope-intercept form.

`\large{y = mx + b}`

Substitute m = 7.

`y = 7x + b`

Step 3

• Substitute any given coordinate points in the rewritten equation.

Substituting any given coordinate points will give the same solution.

Step 3.1

• Substitute (0,12) in the equation.

`y = 7x + b \\ 12 = 7(0) + b \\ 12 = 0 + b \\ 12 = b`

Step 3.2

• Substitute (-4,-16) in the equation.

`y = 7x + b \\ - 16 = 7( - 4) + b \\ - 16 = - 28 + b \\ - 16 + 28 = b \\ 12 = b`

Step 4

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

`y = 7x + b`

Substitute b = 12.

`y = 7x + 12`

Hence, the solution is y = 7x+12.

Hope this helps! Any questions about my answer can be asked in comments.

~ Vectør ~