Write an equation in point-slope form of the line that passes though the given points. Then, write the equation in slope intercept form. (-1,-2) and (2,4)

Question

asked Aug 18, 2022 1.9k views

1 Answer

Jwaliszko · Answer 1 · 2022-08-25T05:28:34+0000

Answer:

Please check the explanation.

Explanation:

Given the points

Finding the slope between (-1, -2) and (2, 4)

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)$

$\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(2,\:4\right)$

$m=(4-\left(-2\right))/(2-\left(-1\right))$

m=2

Using the point-slope form

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 2 and the point (-1, -2)

$y-y_1=m\left(x-x_1\right)$

y -(-2) = 2(x-(-1)

Thus, the point-slope form of the line equation is

y -(-2) = 2(x-(-1)

now, write the slope-intercept form of the line equation y = mx+b

$y-\left(-2\right)=2\left(x-\left(-1\right)\right)$

$y+2=2\left(x+1\right)$

subtract 2 from both sides

$y+2-2=2\left(x+1\right)-2$

Simplify

y=2x+0

y = 2x

Therefore, the equation in slope-intercept form is: