Question

"write an equation in slope-intercept form of the line satisfying the given conditions."

Answer 1

Hi there,

Let's get started,

The line is parallel to the line whose equation is y = 4x + 1.

So the slope will be the same.

The equation that would be possible is :

y = 4x + c

By the way, we know that the line passes through (-3 ; 2).

We just have to substitute these values in the equation in order to find the value of c.

(x ; y) ==> x = -3 and y = 2

Let's do this then,

2 = 4(-3) + c

c = 2 - 4(-3)
c = 2 + 12
c = 14

In short, the answer would be :
y = 4x + 14.

Hope this helps !

Photon

Answer 2

Hey there :)

The line with coordinates ( -3 , 2 ) is parallel to the line y = 4x + 1

Being Parallel means, both have the same slope
The slope is 4

The slope-intercept form is : y = mx + b {m is the slope and b is the y-intercept}

y - y₁ = m ( x - x₁ )

y - 2 = 4 ( x - (-3) )
minus and minus becomes addition
y - 2 = 4 ( x + 3 )
distribute 4 into the parenthesis
y - 2 = 4x + 12
  + 2         + 2

y = 4x + 14