For an equation of a line in the form
y=mx+b,the constant m is the slope of the line. Thus, the line represented by
y=−3x+4 has slope
−3. Lines that are parallel have the same slope. To find out which of the given equations represents a line with the same slope as the line represented by y = −3x + 4, one can rewrite each equation in the form
y=mx+b, that is, solve each equation for y. Choice A,
6x+2y=15, can be rewritten as
2y=−6x+15 by subtracting
6x from each side of the equation. Then, dividing each side of
2y=−6x+15 by 2 gives
y=−x+=−3x+.Therefore, this line has slope −3 and is parallel to the line represented by
y=−3x+4. (The lines are parallel, not coincident, because they have different y-intercepts.)
Choices B, C, and D are incorrect and may be the result of common misunderstandings about which value in the equation of a line represents the slope of the line.