Question

Which equation represents a line that passes through (-2, 4) and has a slope of 1/2?

Answer 1

`\large\boxed{y-4=(1)/(2)(x+2)\text{- point-slope form}}\\\boxed{y=(1)/(2)x+5\text{- slope-intercept form}}`

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

m - slope

We have the slope
`m=(1)/(2)` and the point
`(-2, 4)`.

Substitute:

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

`y-4=(1)/(2)(x+2)` - point-slope form

Convert to the slope-intercept form (y = mx + b):

`y-4=(1)/(2)(x+2)` use the distributive property

`y-4=(1)/(2)x+1` add 4 to both sides

`y=(1)/(2)x+5` - slope-intercept form