# Digital SAT Math: Linear equations in two variables -Practice Questions

## SAT MAth Practice questions – all topics

• Algebra Weightage: 35%  Questions: 13-15
• Linear equations in one variable
• Linear equations in two variables
• Linear functions
• Systems of two linear equations in two variables
• Linear inequalities in one or two variables

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question    Easy

A line in the $$x y$$-plane passes through the point $$(0,5)$$ and has a slope of 7 . What is an equation of this line?
A) $$y=5 x-7$$
B) $$y=5 x+7$$
C) $$y=7 x-5$$
D) $$y=7 x+5$$

Ans:D

A line in the $$xy$$-plane passes through the point $$(0, 5)$$ and has a slope of 7. The equation of a line in slope-intercept form is given by:

$y = mx + b$

where $$m$$ is the slope and $$b$$ is the $$y$$-intercept.

Given:
Slope ($$m$$) = 7
Point $$(0, 5)$$ indicates that the $$y$$-intercept ($$b$$) is 5.

Substituting these values into the slope-intercept form:

$y = 7x + 5$

[Calc]  Question   Easy

The lines shown model the populations of Iowa and Louisiana from 1900 to 2020. In what year does the graph indicate that Iowa and Louisiana had the same population?
A) 1900
B) 1940
C) 1990
D) 2000

Ans:B

To determine the year when Iowa and Louisiana had the same population based on the graph of their population trends from 1900 to 2020, follow these steps:

1. Identify the intersection point of the two lines representing the populations of Iowa and Louisiana.
2. Read the corresponding year from the $$x$$-axis at the intersection point.

[Calc]  Question  Easy

The given graph shows the relationship between the prices during an online sale, where x is the non sale price, in dollars, of an item and y is the total sale price, in dollars, of the item, including a shipping fee.

Which equation represents the relationship between x and y?
A) $y=2x+ 10$
B) $y=2x-10$
C) $$y= \frac{1}{2} x +10$$
D) $$y= \frac{1}{2} x -10$$

C) $$y= \frac{1}{2} x +10$$

To find the equation of a line given the intercept and two points on the line, follow these steps:

The slope $$m$$ of the line passing through points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:
$m = \frac{y_2 – y_1}{x_2 – x_1}$

Using the points $$(20, 20)$$ and $$(60, 40)$$:
$m = \frac{40 – 20}{60 – 20} = \frac{20}{40} = 0.5$

The slope-intercept form of the equation of a line is:
$y = mx + c$

We know $$m = 0.5$$ and the intercept $$c = 10$$:
$y = 0.5x + 10$

[Calc]  Question  Easy

Line $$l$$ has a slope of -3 and an $$x$$-intercept of $$\left(\frac{9}{2}, 0\right)$$. What is the $$y$$-intercept of line $$l$$ ?
A) $$\left(\frac{9}{2}, 0\right)$$
B) $$\left(0, \frac{9}{2}\right)$$
C) $$\left(\frac{27}{2}, 0\right)$$
D) $$\left(0, \frac{27}{2}\right)$$

D

To find the $$y$$-intercept of line $$l$$, we can use the point-slope form of a linear equation:

$y – y_1 = m(x – x_1)$

Where:
$$m$$ is the slope of the line.
$$(x_1, y_1)$$ is a point on the line.

Using the given $$x$$-intercept $$\left(\frac{9}{2}, 0\right)$$ and the slope $$m = -3$$, we have:

$y – 0 = -3(x – \frac{9}{2})$
$y = -3x + \frac{27}{2}$

Now, we need to find the $$y$$-intercept, which occurs when $$x = 0$$:
$y = -3(0) + \frac{27}{2}$
$y = \frac{27}{2}$

So the $$y$$-intercept of line $$l$$ is $$\left(0, \frac{27}{2}\right)$$.

$\boxed{D) \, \left(0, \frac{27}{2}\right)}$

[Calc]  Question Easy

A certain university offers courses that are either 3 credits or 4 credits per course each semester. A student registered for a total of 16 credits for the fall semester. Which equation represents the possible number of 3-credit courses, $x$, and 4-credit courses, $y$, that the student could have registered for?
A) $3 x+4 y=7$
B) $3 x+4 y=16$
C) $x+y=7$
D) $x+y=16$

B

[Calc]  Question  Easy

The graph of linear function $f$ is shown. What is the $y$-intercept of the graph of $f$ ?
A) $(0,0)$
B) $(0,2)$
C) $(0,3)$
D) $(0,6)$

B

[Calc]  Question  Easy

The graph of the linear function $p$ is shown. Which equation defines $p$ ?
A) $p(x)=-3 x+5$
B) $p(x)=-3 x+2$
C) $p(x)=-\frac{1}{3} x+5$
D) $p(x)=-\frac{1}{3} x+2$

A

[Calc]  Question  Easy

$$T=0.32 x+0.29 y$$

Janice raises chickens. She uses the equation shown to estimate the total daily feed intake $\mathrm{T}$, in pounds, for $x$ male and $y$ female chickens that are between 28 and 35 days old.

Using the given equation, Janice estimates that the total daily feed intake for her chickens is 90 pounds. If Janice has 100 male chickens, how many female chickens does she have?
A) 191
B) 200
C) 228
D) 245

B

[Calc]  Question Easy

The table lists selected values of Sam’s walking speed, in kilometers per hour ( $\mathrm{km} / \mathrm{h})$, and his corresponding pulse, in beats per minute (bpm). There is a linear relationship between Sam’s speed, $x$, and his pulse, $f(x)$. Which of the following equations describes $f(x)$ ?
A) $f(x)=x+57$
B) $f(x)=-x+97$
C) $f(x)=5 x+57$
D) $f(x)=-5 x+97$

C

[Calc]  Question Easy

The table above shows some values of $x$ and their corresponding values of $y$. Which of the following equations shows a possible relationship between $x$ and $y$ ?
A) $y=x+2$
B) $y=x-2$
C) $y=2 x+3$
D) $y=3 x-2$

A

Question

A college mathematics department plans to spend 1,800 buying computers and books. Each computer costs 300 and each book costs 90. Which equation represents this situation, where $$x$$ is the number of computers and $$y$$ is the number of books that the department can buy?A. 300$$x$$+ 90$$y$$ = 1,800 1.1
B. 90$$x$$+ 300$$y$$= 1,800
C. 390($$x$$+ $$y$$) = 1,800
D. l,800($$x$$ + $$y$$) = 390

A

Question

$$y$$=($$x$$+5)2-8

The equation above can be represented by a parabola in the $$xy$$-plane. The parabola is then translated so that the vertex is at (O, O). Which of the following best describes the translation? 2.10

1. 5 units in the negative $$x$$ direction and 8 units in the negative $$y$$ direction
2. 5 units in the negative $$x$$ direction and 8 units in the positive $$y$$ direction
3. 5 units in the positive $$x$$ direction and 8 units in the negative $$y$$ direction
4. 5 units in the positive $$x$$ direction and 8 units in the positive $$y$$ direction

D

Question

A hotel has a total of 180 rooms, and on a certain day, half the rooms were cleaned. There were 9 housekeepers on duty at the hotel that day, and each housekeeper cleaned the same number of rooms, r. Which of the following equations represents the information given in terms of r ? 2.14

A

Questions

$f(x)=2 x-11$

The function $f$ is defined above. What is the value of $\mathrm{f}(-2)$ ?
A. -15
B. -7
C. 15
D. 30

Ans: A

Question

A checkers enthusiast is customizing a checkers set by painting a design on each of the 24 checkers in the set. It takes the enthusiast 35 minutes to paint the design on each checker. If $c$ of the checkers are already painted, which of the following represents the number of additional minutes needed to finish painting the set of checkers?
A. $24(35-c)$
B. $24(c-35)$
C. $35(24-c)$
D. $35(c-24)$

Ans: C

Question

$f(x)=\frac{x+3}{2}$

For the function $f$ above, what is the value of $f(7)-f(5)$ ?
A. $\frac{1}{2}$
B. 1
C. 2
D. $\frac{5}{2}$

Ans: B

Question

Ms. Anderson currently has 550 contacts on an online professional networking site. Her goal is to have at least 1,000 contacts. If she wants to meet this goal in 25 weeks, what is the minimum number of contacts per week, on average, she should add?
A. 18
B. 19
C. 21
D. 22

Ans: A

Question

If $3 x=24$, what is the value of $2 x-3$ ?
A. 8
B. 10
C. 11
D. 13

A farmer sold 108 pounds of produce that consisted of $z$ pounds of zucchini and $c$ pounds of cucumbers. The farmer sold the zucchini for $\$ 1.69$per pound and the cucumbers for$\$0.99$ per pound and collected a total of $\$ 150.32$. Which of the following systems of equations can be used to find the number of pounds of zucchini that were sold? A.$z+c=150.321 .69 z+0.99 c=108$B.$z+c=1081.69 z+0.99 c=150.32$C.$z+c=1080.99 z+1.69 c=150.32$D.$z+c=150.320 .99 z+1.69 c=108\$