Question

What is a correct equation for the line passing through the point (-2,1) and having slope m=1/2

Answer 1

Explanation:

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

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

m - slope

We ahve the slope m = 1/2 and the point (-2, 1). Substitute:

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

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

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

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

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

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

Convert to the standard form (Ax + By = C):

`y=(1)/(2)x+2` multiply both sides by 2

`2y=x+4` subtract x from both sides

`-x+2y=4` change the signs

`x-2y=-4` - standard form

Convert to the general form (Ax+By+C=0):

`x-2y=-4` add 4 to both sides

`x-2y+4=0` - general form