Coordinate Geometry
12 . G The slope-intercept form of a line is y = mx + b. To put an equation in this form, isolate y on
the left-hand side of the equation. First, add 3x to each side to get −y = 3x − 7, and then
subtract 7 from each side to get −y = 3x − 7. Now, you just need to multiply (or divide) both
sides by −1 to get 7 = −3x + 7, so the answer is (G). Choices (F), (H), and (J) are similar
versions of the correct answer that each make an error involving a negative sign, either when
adding or subtracting terms from the left side or when multiplying the final equation by −1.
21 . C To find the slope-intercept form of a line, rewrite the equation in the form y = mx + b. Begin
by subtracting 6x from each side of the equation to get 2y − 4 = −6x + 12. Next, add 4 to each
side to get 2y = −6x + 16. Finally, divide each side by 2 to get y = −3x + 8. Choices (A), (B),
and (D) all make mistakes involving negative signs, and (E) switches the coefficient of x
with the constant on the right side of the equation.
22 . K First, find the slope of the line by writing it in slope-intercept form. Subtract 2x from each
side and then divide each side by 5 to get y = x − 2. Perpendicular lines have opposite
reciprocal slopes. Since the slope of the original line is , the negative reciprocal would
be , as in (K). Choice (F) forgets to take the negative reciprocal. Choice (G) is the slope of
a parallel line, and (H) gives the negative of the original slope, but not the negative
reciprocal.
23 . D When finding the slope of a line given in the standard (x,y) coordinate plane, rewrite the
equation in slope-intercept form, which is y = mx + b. In this case, start by adding 5x to each
side of the equation to isolate y, which results in 3y = 5x − 9. Now divide both sides by 3,
giving y = x − 3. In this case, the slope is the coefficient of x, which is . If you chose (B),
be careful: You may have switched some negative signs.
31 . E To find the y-coordinate of the point of intersection of two lines, you need to find values for x
and y that satisfy both equations. Both equations are equal to y, so set the right side of the
first equation equal to the right side of the second equation: 4x + 7 = 6x − 3. Then solve for x
to get −2x = −10, and x = 5. To find the value of y, substitute x = 5 into either of the original
equations. If you use the first equation, for example, y = 4(5) + 7 = 20 + 7 = 27. If you chose
(A) be careful: this is the x-coordinate!
36 . H To find the slope of a line given two points in the standard (x,y) coordinate plane, use the
