write the equation of the line that passes through the point (-2,3) and has a slope of 1/2

Question

write the equation of the line that passes through the point (-2,3) and has a slope of 1/2 in both forms.

Answer 1

Hello, thank you for taking the time to post your question!

Since you’re given the slope and a point on the line I would use point-slope form in order to evaluate this one

y – y1 = m(x – x1) , and in this situation we have (x1,y1) = (-2,3) and m = ½

y – 3 = ½(x - -2)

y – 3 = 1/2x + 1

y = 1/2x + 4

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Diane;

(-2,3) and has a slope of 1/2

Point-slope formula is...

y-y₁=m(x-x₁)

m is slope.

y-3=(1/2)(x--2)

y-3=(1/2)(x+2)

y-3=(1/2)x+1

Add 3 to both sides...

3+y-3=(1/2)x+1+3

y=(1/2)x+4

This is slope-intercept form...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

If you would like this in standard form...

Ax+By=C, A>0

y=(1/2)x+4

Let's subtract (1/2)x from both sides...

-(1/2)x+y=(1/2)x-(1/2)x+4

-(1/2)x+y=4

Bearing in mind the fact that A must be greater than zero, let's multiply both sides by -1...

-1[-(1/2)x+y]=(4)(-1)

(1/2)x-y=-4

Answer 3

To start in point-slope form,

y = mx + b

3 = 1/2(-2) + b

3 = -1 + b

so b = 4

 

Point-slope equation is y = (1/2)x + 4

 

In Standard form,

Ax+Bx = c

first multiply both sides of your equation by 2

2y = x + 8 

substract x from both sides

Standard form equation is 2y - x = 8