slope formula: slope = . Using the points (3,7) and (9,11), slope =
, or (H). If you chose (F) or (G), be careful: You may have forgotten one of
the negatives in the slope formula. If you chose (J), you might have found rather than
.
41 . B In the standard (x,y) coordinate plane, when a function crosses the x-axis, y will be equal to
0. So, you are looking for an equation in which, when x = −3 and when x = 5, y = 0. When
you plug in x = −3 to all the equations, only (B) and (C) result in y = 0. When you plug in x =
5 to those two remaining answer choices, only (B) still gives you y = 0. Choices (A) and (E)
give equations that, when graphed, cross the x-axis at x = 3 and x = −5, and (D) gives an
equation that, when graphed, crosses the x-axis when x = −3 and x = −5.
44 . F To find the slope of a line given two points on the standard (x, y) coordinate plane, use the
formula for slope: slope = . Plug in the given coordinate points into the
equation to get = 3, as in (F). If you chose (H) or (J), you may have found
the slope of a different line. Choice (H) is the slope of , and (G) is the slope of .
45 . D Start by drawing the three sides of the right triangle QRS and find the lengths of its legs.
Since QR is a vertical segment, the length of QR is the difference between the y-coordinates,
or 8 units. Since QS is a horizontal segment, the length of QS is the difference between the x-
coordinates, or 7 units. In all triangles, the shortest side is always opposite the smallest
angle. Therefore, R is the smallest angle because it is opposite the shortest side. To find the
tangent of R, use SOHCAHTOA, which tells you that tanθ = . So tan R = ,
which is (D). If you chose one of the other answers, make sure you are solving for the correct
function. Choice (E) is the tangent of S. Choice (B) is the sine of R, and (C) is the cosine
of R.
59 . A To find which line is parallel to the given line, begin by writing the original equation in
slope-intercept form, or y = mx + b. Start by adding 4x to each side of the equation, giving
you 3y = 4x + 24, and then divide each side by 3 to get y = x + 6. The slope of this equation
is , and any line parallel to this line must also have a slope of . Convert each answer
