Question

A line passes through the point (-3, -3) and has a slope of 1/2. What is the equation of the line? A y= 1/2x + 3/2 B y= 1/2x -3/2 C y= 1/2x -1/2 D y= -1/2x -3/2

Answer 1

`\Large \boxed{\mathrm{Option \ B}}`

Explanation:

y = mx + b

(slope intercept form of a line)

m = slope

b = y-intercept

y = 1/2x + b

Only three options have a slope of 1/2.

y= 1/2x + 3/2

y= 1/2x - 3/2

y= 1/2x - 1/2

The line crosses the point (-3, -3), x = -3 and y = -3.

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

-3= -3/2 + 3/2

-3 = 0

This is false.

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

-3 = -3/2 - 3/2

-3 = -6/2

-3 = -3

This is true.

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

-3 = -3/2 - 1/2

-3 = -2

This is false.

Answer 2

`(B.) y= 1/2x -3/2`

Explanation:

`(-3, -3) = (x_1,y_1)\\m = 1/2\\\\y-y_1=m(x-x_1)\\\\y -(-3)=(1)/(2) (x -(-3)\\\\y+3 = (1)/(2)(x+3)\\\\ y+3 = (1)/(2) x+(3)/(2)\\\\ y = (1)/(2) x +(3)/(2) -3\\\\y = (1)/(2) x - (3)/(2)`