Question

Please help me out with this

Answer 1

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 = $\frac{23+21}{-4-7}$ = $\frac{44}{-11}$ = - 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

Answer 2

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

$y-y_ {0} = m (x-x_ {0})$

Where:

m: It's the slope

$(x_ {0}, y_ {0}):$ It is a point through which the line passes

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

$(x1, y1) :( 7, -21)\\(x2, y2): (- 4,23)$

$m = \frac {y2-y1} {x2-x1} = \frac {23 - (- 21)} {- 4-7} = \frac {44} {- 11} = - 4$

So:

$m = -4\\(x_ {0}, y_ {0}) :( 7, -21)$

Substituting:

$y - (- 21) = - 4 (x-7)\\y + 21 = -4x + 28$

Answer:

$y + 21 = -4x + 28$