Graphing Linear Functions — Free Algebra 1 Review Games.
This unit covers slope, slope-intercept form, x and y intercepts and parallel and perpendicular lines — essential concepts for Algebra 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers slope, slope-intercept form, x and y intercepts and parallel and perpendicular lines — essential concepts for Algebra 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Slope
Slope measures the steepness and direction of a line, calculated as rise over run between any two points. Students must be able to calculate slope from two coordinate pairs using the formula m = (y₂ - y₁) / (x₂ - x₁). A positive slope rises left to right, negative falls, zero is horizontal, and undefined is vertical.
Key Points
- Formula: m = (y₂ - y₁) / (x₂ - x₁); order of subtraction must be consistent
- Horizontal lines have slope = 0; vertical lines have undefined slope
- A slope of 2 means rise 2, run 1 (up 2, right 1)
- Slope is the same between any two points on the same line
Find the slope of the line passing through (1, 3) and (4, 9).
Subtract the y-values and x-values in the same order: m = (9 - 3) / (4 - 1) = 6 / 3 = 2. The slope is 2, meaning for every 1 unit right, the line goes up 2 units. Since the slope is positive, the line rises from left to right.
2 Slope-Intercept Form
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Students must be able to identify m and b from the equation, graph a line using them, and write an equation given slope and a point or two points. This is the most tested form of a linear equation.
Key Points
- y = mx + b: m = slope, b = y-intercept (where line crosses the y-axis)
- To graph: plot the y-intercept first, then use slope (rise/run) to find a second point
- To write the equation: find m first, then substitute one point to solve for b
- Rewrite equations not in slope-intercept form by solving for y
Write the equation of a line with slope -3 that passes through (2, 1).
Start with y = mx + b and substitute m = -3 and the point (2, 1): 1 = -3(2) + b. Simplify to get 1 = -6 + b, so b = 7. The equation is y = -3x + 7.
3 X and Y Intercepts
The y-intercept is where the line crosses the y-axis (x = 0), and the x-intercept is where it crosses the x-axis (y = 0). Students must find both intercepts from an equation and use them to graph a line. Intercept form ax + by = c is commonly tested in this context.
Key Points
- To find the y-intercept: substitute x = 0 into the equation and solve for y
- To find the x-intercept: substitute y = 0 into the equation and solve for x
- Write intercepts as coordinate pairs: y-intercept = (0, b), x-intercept = (a, 0)
- Two intercepts are enough to graph a line — plot both points and draw the line
Find the x- and y-intercepts of 3x + 2y = 12, then graph.
For the y-intercept, set x = 0: 3(0) + 2y = 12 → y = 6, giving point (0, 6). For the x-intercept, set y = 0: 3x + 2(0) = 12 → x = 4, giving point (4, 0). Plot (0, 6) and (4, 0) and draw a straight line through them.
4 Parallel and Perpendicular Lines
Parallel lines have equal slopes and different y-intercepts, so they never intersect. Perpendicular lines have slopes that are negative reciprocals of each other (m₁ × m₂ = -1). Students must identify parallel or perpendicular relationships from equations and write equations of lines parallel or perpendicular to a given line through a given point.
Key Points
- Parallel lines: same slope (m), different b — example: y = 2x + 1 and y = 2x - 5
- Perpendicular lines: slopes are negative reciprocals — flip and change the sign (e.g., 2 and -1/2)
- To write a parallel line: keep the same slope, use the given point to find new b
- To write a perpendicular line: take the negative reciprocal of the slope, then find b
Write the equation of a line perpendicular to y = 4x - 3 that passes through (8, 1).
The slope of the given line is 4, so the perpendicular slope is -1/4 (negative reciprocal). Substitute into y = mx + b using the point (8, 1): 1 = -1/4(8) + b → 1 = -2 + b → b = 3. The equation is y = -1/4x + 3.
Questions, answered.
What is Graphing Linear Functions?
Graphing Linear Functions is Unit 3 of Algebra 1, covering slope, slope-intercept form, x and y intercepts and parallel and perpendicular lines.
How to study for Algebra 1 Unit 3?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.