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