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
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) \(y=7 x+5\)
▶️Answer/Explanation
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:
\[
y = 7x + 5
\]
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
▶️Answer/Explanation
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.
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) \(y= \frac{1}{2} x -10\)
▶️Answer/Explanation
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 \( c = 10 \):
\[
y = 0.5x + 10
\]
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) \(\left(0, \frac{27}{2}\right)\)
▶️Answer/Explanation
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 \(\left(0, \frac{27}{2}\right)\).
Therefore, the answer is:
\[ \boxed{D) \, \left(0, \frac{27}{2}\right)} \]
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) $x+y=16$
▶️Answer/Explanation
B