Complete the equations of the line through (-9,7) and (-6,-3)

In point slope form, the equation is y-7=(-10/3)(x+9). In slope-intercept form, it is y=(-10/3)x-23.

First find the slope of the line. The formula for slope is
m=(y₂-y₁)/(x₂-x₁)

Using our points, we have
m=(-3-7)/(-6--9) = -10/3

Plug this into point slope form:
y-y₁=m(x-x₁)
y-7=(-10/3)(x--9)
y-7=(-10/3)(x+9)

Using the distributive property:
y-7=(-10/3)*x+(-10/3)*9
y-7=(-10/3)x-90/3
y-7=(-10/3)x-30

Add 7 to both sides:
y=(-10/3)x-23

boffeemadrid boffeemadrid · Answer 2 · 2021-11-09T11:24:57+01:00

The equation of the line through the given points is required.

The required equation is [tex]y=-\dfrac{10}{3}x-23[/tex]

The points are

[tex](-9,7)[/tex] and [tex](-6,-3)[/tex]

The equation of a line is given by

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\Rightarrow y-7=\dfrac{-3-7}{-6-(-9)}(x-(-9))\\\Rightarrow y-7=-\dfrac{10}{3}x-30\\\Rightarrow y=-\dfrac{10}{3}x-23[/tex]

The required equation is [tex]y=-\dfrac{10}{3}x-23[/tex]

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