15 Questions
Which of the following represents a linear equation with a slope of 1 and a y-intercept of -7?
y = x - 7
What is the slope and y-intercept of the equation 2x + 5y = 20?
Slope = -2, Y-intercept = -4
Identify the equation of the line graphed below.
2x + y = 4
Write a linear equation given the graph.
y = -3x + 4
Identify the x-intercept of the equation 4x - y = 4.
(4,0)
Which of the following represents the equation of a horizontal line?
$y = -2$
What is the slope-intercept form of a line parallel to the line 5x – 2y = 18 and passing through the point (-2, -1)?
y = 2x + 1
Which line is perpendicular to the line y = -3x + 2?
x + 3y = 24
What is the equation of a line parallel to y = -4x + 5 and passing through the point (-2, -1)?
y = 2x + 1
What is the equation of a line perpendicular to 3x – 5y = 5 and passing through the point (9, -14)?
x + 3y = 24
Use the line of best fit to predict the number of students enrolled in Beach Manor Preschool in 2010.
95
Estimate Luke’s golf score for week 12 using the line of best fit.
75
How many prints can MaryAnn order from the online print shop if she has $35 to spend?
200 prints
How much did the Jones Family pay for renting a boat from Smith Mountain Lake Boat Rentals?
$185.50
If Alaina sold 15 poinsettias and made $543, how many wreaths did she sell?
20 wreaths
Study Notes
Linear Equations
- A linear equation with a slope of 1 and a y-intercept of -7 is represented by the equation y = x - 7
- The slope and y-intercept of the equation 2x + 5y = 20 can be found by rewriting it in slope-intercept form (y = mx + b), giving a slope of -2/5 and a y-intercept of 4
Graphing Lines
- The equation of a line graphed can be written in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1)) given the graph
Intercepts
- The x-intercept of the equation 4x - y = 4 is the point where the line intersects the x-axis, found by setting y = 0 and solving for x
Horizontal Lines
- A horizontal line has a slope of 0 and can be represented by the equation y = k, where k is the y-intercept
Parallel and Perpendicular Lines
- The slope-intercept form of a line parallel to the line 5x – 2y = 18 and passing through the point (-2, -1) can be found by first rewriting the original equation in slope-intercept form and then using the same slope and the given point
- The equation of a line perpendicular to the line y = -3x + 2 has a slope that is the negative reciprocal of -3
- The equation of a line parallel to y = -4x + 5 and passing through the point (-2, -1) has the same slope as the original line
- The equation of a line perpendicular to 3x – 5y = 5 and passing through the point (9, -14) has a slope that is the negative reciprocal of the slope of the original line
Applications of Linear Equations
- The line of best fit can be used to predict the number of students enrolled in Beach Manor Preschool in 2010
- The line of best fit can be used to estimate Luke’s golf score for week 12
- Linear equations can be used to solve real-world problems, such as finding the number of prints MaryAnn can order from an online print shop given a budget of $35
- Linear equations can be used to solve real-world problems, such as finding the cost of renting a boat from Smith Mountain Lake Boat Rentals for the Jones Family
- Linear equations can be used to solve real-world problems, such as finding the number of wreaths Alaina sold if she sold 15 poinsettias and made $543
Prepare for your Unit 4 Linear Equations test with this study guide, covering topics such as slope, slope-intercept form, and standard form of linear equations. Practice writing linear equations, identifying slopes and y-intercepts, and more.
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