Mathematics: What is an equation of the line that passes through the points (6, -7) and (-6, 3))? Put your answer in fully reduced form.

-3,2 is the answerStep-by-step explanation:hope you like it...

What is an equation of the line that passes through

mayaparness

12.02.2022

The equation of the line is y = $-\frac{5}{6}$ x - 2

Step-by-step explanation:

The form of the linear function is y = m x + b, where

m is the slopeb is the y-intercept

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (6, -7) and (-6, 3)

∴ x1 = 6 and y1 = -7

∴ x2 = -6 and y2 = 3

→ Substitute them in the rule of the slope above to find it

∵ m = $\frac{3--7}{-6-6}$ = $\frac{3+7}{-12}$ = $\frac{10}{-12}$ = $\frac{5}{-6}$

∴ m = $-\frac{5}{6}$

→ Substitute it in the form of the equation above

∴ y = $-\frac{5}{6}$ x + b

→ Substitute x and y in the equation by x1 and y1

∵ x1 = 6 and y1 = -7

∴ -7 = $-\frac{5}{6}$ (6) + b

∴ -7 = -5 + b

→ Add 5 to both sides

∵ -7 + 5 = -5 + 5 + b

∴ -2 = b

→ Substitute the value of b in the equation

∴ y = $-\frac{5}{6}$ x + -2

∴ y = $-\frac{5}{6}$ x - 2

∴ The equation of the line is y = $-\frac{5}{6}$ x - 2

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