Question

A line has a slope of -1/2 and a y-intercept of 3.

Which equations represent the line?

Choose all answers that are correct.

A. 2y=6+x


B. x+2y=6


C. y= -1/2+3


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

Answer 1

Slope Intercept Form: y = mx + b
(x, y) --> point on the line
m --> slope
b --> y-intercept

Point Slope Form: (y - y1) = m (x - x1)
(x1, y1) --> point on the line
m --> slope

Now that we know that information, we can substitute in what we know.
Slope Intercept Form: y = -1/2x + 3

Any equation will have to simplify to the equation above if it is an equation of the line.

A. 2y = 6 + x
y = 6/2 + x/2
y = 3 + 1/2x
Not an equation.

B. x + 2y = 6
2y = 6 - x
y = 6/2 - x/2
y = 3 - 1/2x
y = -1/2x + 3
Equation.

C. y = -1/2x + 3
Equation.

D. (y - 2) = -1/2 (x - 2)
y - 2 = -1/2x + 1
y = -1/2x + 3
Equation.

B, C, and D are all equations that represent the line.