What is the equation in standard form of the line which passes through (-2, -3) and has a slope of 1/2?

Question

What is the equation in standard form of the line which passes through (-2, -3) and has a slope of 1/2?

Choose one answer.

A. 2x + y = 4
 

B. 2x - y = 4
 

C. x + 2y = 4
 

D. x - 2y = 4

Answer 1

Another way to solve this is to use the point-slope formula:  m(x-x₁) = y-y₁

m(x-x1) = y-y1   (-2, -3)  m = 1/2

 

substitute the values

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

 

simplify

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

 

multiply both sides by 2 to get rid of the fraction

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

 

simplify

x + 2 = 2y + 6

 

subtract 4 from both sides

x = 2y + 4

 

subtract 2y from both sides

x - 2y = 4    answer: d

 

hope this helps

 

 

Answer 2

OK, May, here we go.

 

Let's start with slope-intercept form, y = mx + b so we can find b.

 

Put in the given info, using our point, so we can find the value of b.

 

-3 = (1/2)(-2) + b

-3 = -1 + b

-2 = b

 

So, we have y = (1/2)x - 2

 

Move things around to get (1/2)x - y = 2

 

That doesn't look quite like any of our choices, but remember that a multiple of an equation gives us the same line, so we can multiply the entire thing by 2.

 

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

          x - 2y = 4

 

Our answer is D.

 

Let's check.  

 

-2 - (2(-3)) = 4

    -2 - (-6) = 4

       -2 + 6 = 4

               4 = 4

 

Check!

    

 

Hope this helps!