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Find an equation for the line that passes through the points (-6, 3) and (6, -6).

Sagot :

slope=-9/12 = -3/4

y=mx+b y=-3/4x+b

3=-3/4(-6)+b

b=3+9/2=7.5

Equation is y=-0.75x+7.5
nabeelahmed1721

Answer:

[tex]y = -\frac{3}{4}x-\frac{3}{2}[/tex]

Step-by-step explanation:

First, calculate the slope of the line:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{(-6) - 3}{6 - (-6)}\\m = \frac{-9}{12}\\m = \frac{-3}{4}[/tex]

Next, calculate the y-intercept:

Choose any point on the line.

[tex](-6,3)[/tex]

Solve for [tex]b[/tex].

[tex]y = mx + b\\b = y - (mx)\\b = 3 - (\frac{-3}{4} * -6)\\b = 3 - \frac{9}{2}\\b = \frac{-3}{2}[/tex]

Finally, create the equation:

 [tex]y = -\frac{3}{4}x-\frac{3}{2}[/tex]

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