Algebra 1 Unit 4: Linear Equations Review

Questions and Answers

In the linear equation $y = \frac{3}{4}x - 1$, what is the slope?

m = \frac{3}{4}

What is the slope of a horizontal line?

m = 0

What is the slope of a vertical line?

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What is the slope of a line that contains the points $(-6, 1)$ and $(4, -4)$?

m = -\frac{1}{2} Signup and view all the answers

What is the slope of the line whose equation is $2y = 3x + 4$?

m = \frac{3}{2} Signup and view all the answers

Convert the equation $x - 4y = 8$ to slope-intercept form.

y = \frac{1}{4}x - 2 Signup and view all the answers

What is the x-intercept of the equation $10x + 4y = -20$?

(-2, 0) Signup and view all the answers

What is the y-intercept of the equation $10x + 4y = -20$?

(0, -5) Signup and view all the answers

What type of line is formed by the equation $y = -2$?

horizontal Signup and view all the answers

What type of line is formed by the equation $x = 7$?

vertical Signup and view all the answers

Write the slope-intercept form equation for the line that passes through the point $(2, -1)$ and has a slope of -3.

y = -3x + 5 Signup and view all the answers

Write the slope-intercept form equation for the line that passes through the point $(-4, -9)$ and has a slope of $\frac{1}{2}$.

y = \frac{1}{2}x - 7 Signup and view all the answers

Write the slope-intercept form equation for the line that passes through the points $(-4, 3)$ and $(2, -6)$?

y = -\frac{3}{2}x - 3 Signup and view all the answers

What is the equation of the line that passes through the points $(-4, 8)$ and $(1, 3)$?

y = -x + 4 Signup and view all the answers

What is the slope of a line parallel to the line $4x + y = 5$?

m = -4 Signup and view all the answers

Which of the following equations represents a line parallel to the y-axis? $y = x$ OR $x = 4$ OR $y = 4$ OR $y = x + 4$

x = 4 Signup and view all the answers

Which of the following equations represents a line perpendicular to the y-axis? $y = x$ OR $x = 4$ OR $y = 4$ OR $y = x + 4$

y = 4 Signup and view all the answers

What is the slope of a line perpendicular to the line $5x - 3y = 27$?

m = -\frac{3}{5} Signup and view all the answers

What is the slope of a line that passes through the point $(3, -1)$ and is perpendicular to the line with an equation $y = -3x + 8$?

m = \frac{1}{3} Signup and view all the answers

Using the line of best fit, which is closest to the length of time it should take Marsha's 8-year-old son to run one lap?

176 Signup and view all the answers

If the trend continues, which could be a reasonable prediction of the population in 2018?

8.72 Signup and view all the answers

Write and solve a linear equation to find the total cost to rent the snowboard from 8:30 a.m. to 12:30 p.m., given the resort charges $15.75 per hour in addition to a $25 deposit.

88 Signup and view all the answers

Write and solve a linear equation to find the cost to rent the shoes if Brandon played 5 games and paid $32 at $4.95 per game.

7.25 Signup and view all the answers

Write and solve a linear equation to find the monthly rent for a 1500 square foot office, given the rent for an 800 square foot office is $975 and for an 1100 square foot office is $1125.

1325 Signup and view all the answers

If Brielle has 66 nickels and the total value in her piggy bank is $7.80, write and solve a linear equation to find the number of dimes she has.

45 Signup and view all the answers

Direct, Inverse or Neither: $\frac{y}{3} = x$?

Direct Signup and view all the answers

Direct, Inverse or Neither: $xy = 40$?

Inverse Signup and view all the answers

Direct, Inverse or Neither: $8x - 2y = 2$?

Neither Signup and view all the answers

If the point $(2, -10)$ lies on the graph of an inverse variation, what is the constant of variation?

k = -20 Signup and view all the answers

If the point $(12, 4)$ lies on the graph of a direct variation, what is the constant of variation?

k = \frac{1}{3} Signup and view all the answers

If $y$ varies directly as $x$ and $y = 3$ when $x = 12$, what is the value of $y$ when $x = 18$?

4.5 Signup and view all the answers

Study Notes

Slope and Line Types

Slope of the line in the equation y = 3/4x - 1 is m = 3/4.
Horizontal lines have a slope of m = 0.
Vertical lines have an undefined slope.
Slope between points (-6, 1) and (4, -4) is m = -1/2.
Line described by 2y = 3x + 4 has a slope m = 3/2.

Slope-Intercept Form

Convert line x - 4y = 8 to slope-intercept form: y = 1/4x - 2.
Line that passes through (2, -1) with slope -3 is: y = -3x + 5.
Line passing through (-4, -9) with a slope of 1/2 is: y = 1/2x - 7.
Line through points (-4, 3) and (2, -6) results in slope-intercept form: y = -3/2x - 3.
Equation of line through points (-4, 8) and (1, 3) is: y = -x + 4.

Parallel and Perpendicular Slopes

Slope of a line parallel to 4x + y = 5 is m = -4.
Equation x = 4 represents a line parallel to the y-axis.
Equation y = 4 represents a line perpendicular to the y-axis.
Slope of line perpendicular to 5x - 3y = 27 is m = -3/5.
Slope of line through (3, -1) perpendicular to y = -3x + 8 is m = 1/3.

Graphing and Predictions

Based on time and age data, a prediction for an 8-year-old's time to run a lap is 176 seconds.
From provided population data, reasonable prediction for Virginia's population in 2018 is 8.72 million.

Linear Equations and Costs

Total cost for snowboard rental from 8:30 a.m. to 12:30 p.m. is $88.
Cost calculation for bowling shoes where Brandon played 5 games and paid $32 results in a shoe rental cost of $7.25.
Monthly rent for a 1500 square foot office is predicted to be $1325.

Word Problems and Equations

Brielle has a total of $7.80 with 66 nickels, leading to 45 dimes.
Identifying types of variation: y/3 = x is a Direct variation; xy = 40 is Inverse; and 8x - 2y = 2 is Neither variation.
Inverse variation constant k for point (2, -10) is k = -20.
Direct variation constant k for point (12, 4) is k = 1/3.
When y varies directly as x, with y = 3 when x = 12, the value of y when x = 18 is 4.5.

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Description

Test your knowledge on linear equations with this flashcard review for Algebra 1 Unit 4. Covering slopes, including horizontal and vertical lines, and calculating slopes from points on a graph, this quiz helps reinforce your understanding of key concepts in this unit.