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VectorFundament120

Answer:

[tex] \large \boxed{y = 7x + 12}[/tex]

Step-by-step 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

[tex] \large{m = \frac{y_2-y_1}{x_2-x_1}}[/tex]

Substitute the coordinate points in the formula.

[tex]m = \frac{12 - ( - 16)}{0 - ( - 4)} \\ m = \frac{12 + 16}{0 + 4} \\ m = \frac{28}{4} \longrightarrow \frac{7}{1} \\ m = 7[/tex]

Step 2

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

[tex] \large{y = mx + b}[/tex]

Substitute m = 7.

[tex]y = 7x + b[/tex]

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.

[tex]y = 7x + b \\ 12 = 7(0) + b \\ 12 = 0 + b \\ 12 = b[/tex]

Step 3.2

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

[tex]y = 7x + b \\ - 16 = 7( - 4) + b \\ - 16 = - 28 + b \\ - 16 + 28 = b \\ 12 = b[/tex]

Step 4

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

[tex]y = 7x + b[/tex]

Substitute b = 12.

[tex]y = 7x + 12[/tex]

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

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

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