Question

What is the equation in slope-intercept form for the line that passes through the points (-2,-1) and (1,5) ?

Answer 1

Answer:

y = 2x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 1) and (x₂, y₂ ) = (1, 5)

m = $\frac{5+1}{1+2}$ = $\frac{6}{3}$ = 2, thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 5), then

5 = 2 + c ⇒ c = 5 - 2 = 3

y = 2x + 3 ← equation of line

Answer 2

Answer: y = 2x + 3

Step-by-step explanation:

The formula for finding equation of line when two points are given is :

$\frac{y-y_{1} }{x-x_{1}}$ = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$x_{1}$ = -2

$x_{2}$ = 1

$y_{1}$ = -1

$y_{2}$ = 5

Substituting the values into the equation , we have

$\frac{y-(-1)}{x-(-2)}$ = $\frac{5-(-1)}{1-(-2)}$

$\frac{y+1}{x+2}$ = $\frac{5+1}{1+2}$

$\frac{y+1}{x+2}$ = $\frac{6}{3}$

$\frac{y+1}{x+2}$ = $\frac{2}{1}$

cross multiplying , we have

y + 1 = 2(x+2)

y + 1 = 2x + 4

in order to write it in slope - intercept form , we will make y the subject of formula , that is

y = 2x + 4 - 1

y = 2x + 3