Question

Find an equation for the line that passes through the points (-3,-2) and (1,4)

Answer 1

Answer:

y=2/3x

Step-by-step explanation:

First, we have to find the slope, which is $\frac{(y_{1} -y_{2})}{(x_{1}-x_{2}}$

(-3-1)/(-2-4)

-4/-6

2/3 is slope.

y=2/3x+-___

substitute in -3 from first point

y=-2+__=-2

y=2/3x+0

y=2/3x

Answer 2

Answer:

y + 2 = (3/2) (x+3)    (point slope form)

Step-by-step explanation:

(see attached for reference)

Given

(x₁, y₁) = (-3,-2)

(x₂, y₂) = (1,4)

Since we are given 2 points, it would be easiest to express the equation of the line in point-slope form (see attached)

(y - y₁) = m (x - x₁)

we already have the values for x₁ and y₁, hence we only need to find the slope m (see 2nd attached graphic)

m = (y₂-y₁) / (x₂ - x₁)

= [4 - (-2) ] / [1 - (-3)]

= (4+2) / (1+3)

= 6/4

= 3/2

substituting the value for m and the values for x₁ and y₁:

(y - y₁) = m (x - x₁)

[y - (-2)] = (3/2) [x - (-3)]

y + 2 = (3/2) (x+3)