Topic 1: Finding x- and y-intercepts given the graph of a line on a grid
- Identify the x- and y-intercepts of a line passing through (2, 0) and (0, 4) on a grid: x-intercept: (2, 0), y-intercept: (0, 4).
- Find the x- and y-intercepts of a line crossing the x-axis at (-3, 0) and the y-axis at (0, 6): x-intercept: (-3, 0), y-intercept: (0, 6).
Topic 2: Finding intercepts of a nonlinear function given its graph
- Determine the x- and y-intercepts of a parabolic graph crossing the x-axis at (1, 0) and (3, 0) and the y-axis at (0, 2): x-intercepts: (1, 0), (3, 0), y-intercept: (0, 2).
- Find the x- and y-intercepts of a nonlinear graph passing through (0, -1), (-2, 0), and (2, 0): x-intercepts: (-2, 0), (2, 0), y-intercept: (0, -1).
Topic 3: Table for a linear function
- Create a table of values for the linear function y = 2x + 1 for x = -2, -1, 0, 1, 2: (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5).
X | Y |
-2 | |
-1 | |
0 | |
1 | |
2 |
- Complete a table for the linear function y = -3x + 4 for x = -1, 0, 1, 2, 3: (-1, 7), (0, 4), (1, 1), (2, -2), (3, -5).
Topic 4: Finding outputs of a two-step function with decimals that models a real-world situation: Function notation
- A taxi fare is given by f(d) = 2.5d + 3.50, where d is miles driven. Find f(4.2): f(4.2) = $14.00.
- The cost of a phone plan is f(m) = 0.15m + 10, where m is minutes used. Find f(20.5): f(20.5) = $13.075.
Topic 5: Graphing a linear equation of the form y = mx
- Graph the linear equation y = 3x on a coordinate plane: Plot points like (0, 0), (1, 3), (2, 6) and draw a line.
- Graph the linear equation y = -2x on a coordinate plane: Plot points like (0, 0), (1, -2), (2, -4) and draw a line.
Topic 6: Graphing a line given its equation in slope-intercept form: Fractional slope
- Graph the line y = (2/3)x + 1 on a coordinate plane: Start at (0, 1), rise 2, run 3.
- Graph the line y = (-1/2)x - 3 on a coordinate plane: Start at (0, -3), fall 1, run 2.
Topic 7: Graphing a vertical or horizontal line
- Graph the vertical line x = 4 on a coordinate plane: Draw a vertical line through x = 4.
- Graph the horizontal line y = -2 on a coordinate plane: Draw a horizontal line through y = -2.
Topic 8: Finding x- and y-intercepts of a line given the equation: Basic
- Find the x- and y-intercepts of the line 2x + 3y = 6: x-intercept: (3, 0), y-intercept: (0, 2).
- Determine the x- and y-intercepts of the line 4x - y = 8: x-intercept: (2, 0), y-intercept: (0, -8).
Topic 9: Classifying slopes given graphs of lines
Topic 10: Finding slope given the graph of a line on a grid
- Find the slope of a line on a grid passing through (1, 2) and (3, 6): m = 2.
- Determine the slope of a line on a grid passing through (-2, 4) and (1, -2): m = -2.
Topic 11: Finding slope given two points on a line
- Calculate the slope of a line passing through (2, 5) and (4, 9): m = 2.
- Find the slope of a line passing through (-1, 3) and (2, -3): m = -2.
Topic 12: Finding the slopes of horizontal and vertical lines
- Determine the slope of the horizontal line y = 5: m = 0.
- Find the slope of the vertical line x = -3: Undefined.
Topic 13: Graphing a line given its slope and y-intercept
- Graph a line with a slope of 2 and a y-intercept of (0, 3): Start at (0, 3), rise 2, run 1.
- Graph a line with a slope of -1 and a y-intercept of (0, -4): Start at (0, -4), fall 1, run 1.
Topic 14: Finding the slope and y-intercept of a line given its equation in the form y = mx + b
- Identify the slope and y-intercept of the equation y = 4x - 2: Slope: 4, y-intercept: (0, -2).
- Find the slope and y-intercept of the equation y = (-3/2)x + 5: Slope: -3/2, y-intercept: (0, 5).
Topic 15: Graphing a line by first finding its slope and y-intercept
- Graph the line y = 2x + 3 by finding its slope and y-intercept: Slope: 2, y-intercept: (0, 3).
- Graph the line y = (-1/3)x - 2 by finding its slope and y-intercept: Slope: -1/3, y-intercept: (0, -2).
Topic 16: Writing an equation in slope-intercept form given the slope and a point
- Write the equation of a line in slope-intercept form with a slope of 3 passing through (1, 4): y = 3x + 1.
- Write the equation of a line in slope-intercept form with a slope of -1/2 passing through (2, -1)
Topic 17: Word problem involving average rate of change
- A car travels 120 miles in 2 hours. Find the average rate of change: 60 miles per hour.
- A tank fills with 60 gallons of water in 3 minutes. Calculate the average rate of change: 20 gallons per minute.
Topic 18: Sketching the line of best fit
Topic 19: Scatter plots and correlation
Topic 20: Graphing a function of the form f(x) = ax + b: Integer slope
- Graph the function f(x) = 2x + 1 on a coordinate plane: Plot (0, 1), (1, 3), (2, 5), draw a line.
- Graph the function f(x) = -3x + 4 on a coordinate plane: Plot (0, 4), (1, 1), (2, -2), draw a line.
Topic 21: Writing an equation and graphing a line given its slope and y-intercept
- Write the equation of a line with a slope of 1 and y-intercept of (0, 2), then graph it: y = x + 2.
- Write the equation of a line with a slope of -4 and y-intercept of (0, 3), then graph it: y = -4x + 3.