SAT CollegeBoard Practice Test (1-8) Coordinate Geometry

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1. (Test2/Q 6/No Calculator)

In the $x y$-plane above, line $\ell$ is parallel to line $k$. What is the value of $p$ ?
A) 4
B) 5
C) 8
D) 10



2. (Test2/Q 9/No Calculator)

The graph of a line in the $x y$-plane has slope 2 and contains the point $(1,8)$. The graph of a second line passes through the points $(1,2)$ and $(2,1)$. If the two lines intersect at the point $(a, b)$, what is the value of $a+b$ ?
A) 4
B) 3
C) $-1$
D) $-4$



3. (Test2/Q 25/Calculator)

The graph of the linear function $f$ has intercepts at $(a, 0)$ and $(0, b)$ in the $x y$-plane. If $a+b=0$ and $a \neq b$, which of the following is true about the slope of the graph of $f$ ?
A) It is positive.
B) It is negative.
C) It equals zero.
D) It is undefined.



4. (Test2/Q 28/Calculator)

In the xy-plane above, $A B C D$ is a square and point $E$ is the center of the square. The coordinates of points $C$ and $E$ are $(7,2)$ and $(1,0)$, respectively. Which of the following is an equation of the line that passes through points $B$ and $D$ ?
A) $y=-3 x-1$
B) $y=-3(x-1)$
C) $y=-\frac{1}{3} x+4$
D) $y=-\frac{1}{3} x-1$



5. (Test $3 / Q 8 /$ No Calculator)

The line $y=k x+4$, where $k$ is a constant, is graphed in the $x y$-plane. If the line contains the point $(c, d)$, where $c \neq 0$ and $d \neq 0$, what is the slope of the line in terms of $c$ and $d$ ?
A) $\frac{d-4}{c}$
B) $\frac{c-4}{d}$
C) $\frac{4-d}{c}$
D) $\frac{4-c}{d}$



6. (Test3/Q 26/Calculator)

In the $x y$-plane, the line determined by the points $(2, k)$ and $(k, 32)$ passes through the origin. Which of the following could be the value of $k$ ?
A) 0
B) 4
C) 8
D) 16



7. (Test $4 / Q 8 /$ No Calculator)

Which of the following equations represents a line that is parallel to the line with equation $y=-3 x+4$ ?
A) $6 x+2 y=15$
B) $3 x-y=7$
C) $2 x-3 y=6$
D) $x+3 y=1$



8. (Test $4 / Q 8 /$ Calculator)

Line $\ell$ in the $x y$-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the following must be true?
A) The slope of line $\ell$ is undefined.
B) The slope of line $\ell$ is zero.
C) The slope of line $\ell$ is positive.
D) The slope of line $\ell$ is negative.



9. (Test $5 / Q 1 /$ No Calculator)

Which of the following is an equation of line $\ell$ in the $x y$-plane above?
A) $x=1$
B) $y=1$
C) $y=x$
D) $y=x+1$



10. (Test5/Q 11/Calculator)

$$-2 x+3 y=6$$ In the $x y$-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
A) $3 x+2 y=6$
B) $3 x+4 y=6$
C) $2 x+4 y=6$
D) $2 x+6 y=3$



11. (Test5/Q 28/Calculator)

The graph of the linear function $f$ is shown in the $x y$-plane above. The slope of the graph of the linear function $g$ is 4 times the slope of the graph of $f$. If the graph of $g$ passes through the point $(0,-4)$, what is the value of $g(9)$ ?
A) 5
B) 9
C) 14
D) 18



12. (Test5/Q 34/Calculator)

In the $x y$-plane, the point $(2,5)$ lies on the graph of the function $f$. If $f(x)=k-x^{2}$, where $k$ is a constant, what is the value of $k$ ?



13. (Test $6 / Q 35 /$ Calculator)

The line with the equation $\frac{4}{5} x+\frac{1}{3} y=1$ is graphed in the $x y$ "plane. What is the $x$-coordinate of the $x$-intercept of the line?



14. (Test7/Q 19/No Calculator)

The graph of a line in the $x y$-plane passes through the point $(1,4)$ and crosses the $x$-axis at the point $(2,0)$. The line crosses the $y$-axis at the point $(0, b)$. What is the value of $b$ ?



15. (Test7/Q $28 /$ Calculator)

In the $x y$-plane above, a point (not shown) with coordinates $(s, t)$ lies on the graph of the linear function $f$. If $s$ and $t$ are positive integers, what is the ratio of $t$ to $s$ ?
A) 1 to 3
B) 1 to 2
C) 2 to 1
D) 3 to 1



16. (Test $7 / Q$ 32/Calculator)

Line $t$ is shown in the $x y$-plane below. What is the slope of line $t$ ?



17. (Test $8 / Q 7 /$ Calculator )

In the $x y$-plane, the graph of which of the following equations is a line with a slope of 3 ?
A) $y=\frac{1}{3} x$
B) $y=x-3$
C) $y=3 x+2$
D) $y=6 x+3$



18. (Test8/Q $27 /$ Calculator)

In the $x y$-plane, the point $(p, r)$ lies on the line with equation $y=x+b$, where $b$ is a constant. The point with coordinates $(2 p, 5 r)$ lies on the line with equation $y=2 x+b$. If $p \neq 0$, what is the value of $\frac{r}{p}$ ?
A) $\frac{2}{5}$
B) $\frac{3}{4}$
C) $\frac{4}{3}$
D) $\frac{5}{2}$



19. (Test8/Q $33 /$ Calculator)

In the $x y$-plane, the equations $x+2 y=10$ and $3 x+6 y=c$ represent the same line for some constant $c .$ What is the value of $c$ ?



20. (Test1/Q 12/No Calculator)

A line in the $x y$-plane passes through the origin and has a slope of $\frac{1}{7}$. Which of the following points lies on the line?
A) $(0,7)$
B) $(1,7)$
C) $(7,7)$
D) $(14,2)$



Answer

1 D$\quad$ Explanation
2 B$\quad$ Explanation
3 A$\quad$ Explanation
4 B$\quad$ Explanation
5 A$\quad$ Explanation
6 C$\quad$ Explanation
7 A$\quad$ Explanation
8 D$\quad$ Explanation
9 D$\quad$ Explanation
10 A$\quad$ Explanation
11 C$\quad$ Explanation
12 9$\quad$ Explanation
13 1.25$\quad$ Explanation
14 8$\quad$ Explanation
15 C$\quad$ Explanation
16 0.4$\quad$ Explanation
17 C$\quad$ Explanation
18 B$\quad$ Explanation
19 30$\quad$ Explanation
20 D$\quad$ Explanation

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