Question

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

Answer 1

Step-by-step 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:

$y-1=\dfrac{1}{2}(x-(-2))$

$y-1=\dfrac{1}{2}(x+2)$ - point-slope form

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

$y-1=\dfrac{1}{2}(x+2)$          use the distributive property

$y-1=\dfrac{1}{2}x+1$          add 1 to both sides

$y=\dfrac{1}{2}x+2$   - slope-intercept form

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

$y=\dfrac{1}{2}x+2$     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