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carlosego

For this case we have that by definition, the point-slope equation is of the form:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes

We find the slope of the line according to the given points:

[tex](x1, y1) :( 7, -21)\\(x2, y2): (- 4,23)[/tex]

[tex]m = \frac {y2-y1} {x2-x1} = \frac {23 - (- 21)} {- 4-7} = \frac {44} {- 11} = - 4[/tex]

So:

[tex]m = -4\\(x_ {0}, y_ {0}) :( 7, -21)[/tex]

Substituting:

[tex]y - (- 21) = - 4 (x-7)\\y + 21 = -4x + 28[/tex]

Answer:

[tex]y + 21 = -4x + 28[/tex]

Answer:

y = - 4x + 28

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (7, - 21) and (x₂, y₂ ) = (- 4, 23)

m = [tex]\frac{23+21}{-4-7}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4

Using m = - 4 and (a, b ) = (7, - 21), then

y + 21 = - 4(x - 7) ← in point- slope form

Distribute right side and simplify

y + 21 = - 4x + 28 ← in slope- intercept form

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