SAT Mathematics Practice Test 4

For an equation of a line in the form $\mathit{y}=\mathit{m}\mathit{x}+\mathit{b},$the constant m is the slope of the line. Thus, the line represented by $\mathit{y}=-3\mathit{x}+4$ 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 $\mathit{y}=\mathit{m}\mathit{x}+\mathit{b},$ that is, solve each equation for y. Choice A, $6\mathit{x}+2\mathit{y}=15$, can be rewritten as $2\mathit{y}=-6\mathit{x}+15$ by subtracting $6\mathit{x}$ from each side of the equation. Then, dividing each side of $2\mathit{y}=-6\mathit{x}+15$ by 2 gives $\mathit{y}=-\frac{6}{2}\mathit{x}+\frac{15}{2}=-3\mathit{x}+\frac{15}{2}$.Therefore, this line has slope −3 and is parallel to the line represented by $\mathit{y}=-3\mathit{x}+4$. (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.