How do you draw the line that is parallel to y=-1/2x+5y=12x+5 and passes through the point (2, -3)?

1 Answer
Mar 26, 2018

The equation of the line parallel to y = -1/2x+5y=12x+5 that passes through the point (2, -3)(2,3) is y = -1/2x-2y=12x2.

Explanation:

The slope of the line parallel to another line is the same as that of the other line. Therefore, the slope of the line parallel to y=-1/2x+5y=12x+5 is -1/212 because the slope of that line is -1/212.

Using point-slope form, y - y_1 = m(x-x_1)yy1=m(xx1) where y-1y1 and x_1x1 are points from a given coordinate pair (x,y)(x,y) that lies on the line, and mm is the slope.

Plugging in -1/212 for mm, 22 for x_1x1, and -33 for y_1y1:
y-(-3) = -1/2(x-2)y(3)=12(x2)
y + 3 = -1/2x + 1y+3=12x+1
y = -1/2x -2y=12x2