I. Slope. The slope of a line measures its steepness. You can use a varitety of methods to determine the slope of a line.
1. Move the blue slider from position 0 to position 1. Move points A and B so that they lie on the new line.
Calculate the slope of the line (you can check your answer using the checkbox).
2. Repeat, moving the blue slider to position 2, 3, 4, and 5.
3. Define slope. Give as many definitions for slope as you can.
4. Explain how to find the slope of a line using a graph.
5. Explain how to find the slope of a line given two points (ordered pairs) on a line.
6. When is the slope of a line positive? When is it negative? When does it equal zero? When is it undefined?
Practice Activity 1: Finding the Slope of a Line I
Practice Activity 2: Finding the Slope of a Line II
Practice Activity 3: Finding the Slope of a Line III
II. Lines and Slopes. You can use the slope (and one additional point) to write the equation of a line. One way to write a linear equation is in slope-intercept form.
1. Use the slider to increase the value of m. Describe the result on the graph.
2. Use the slider to decrease the value of m. Describe the result on the graph.
3. Use the slider to increase the value of b. Describe the result on the graph.
4. Use the slider to decrease the value of b. Describe the result on the graph.
5. Explain why an equation of the form y=mx+b is called slope-intercept form.
Practice Activity 4: Slope-Intercept Form I
Practice Activity 5: Slope-Intercept Form II
Practice Activity 6: Graphing Lines in Slope-Intercept Form
III. Standard Form. Another way to write a linear equations is in standard form: Ax+By=C.
1. Begin with the line having a y-intercept at 6 and an x-intercept at -3. Use the equation to find the value of y when x=0.
Use the equation to find the value of x when y=0.
2. Write the equation in slope-intercept form.
3. Use the sliders to change points R and S. Use the equation to find the value of y when x=0.
Use the equation to find the value of x when y=0. Is this a coincidence? Explain.
4. Write the equation in slope-intercept form. Enter the equation into the Input bar to check your work.
IV. Graphing Linear Equations.
1. Write the equation of a line passing through points A(3,4) and B(0,1). Enter your equation in the Input bar to check your work.
Hit refresh to clear your work.
2. Write the equation of a line passing through points A(5,0) and B(0,-2). Enter your equation in the Input bar to check your work.
Hit refresh to clear your work.
3. Write the equation of a line passing through points A(-3,3) and B(4,-1). Enter your equation in the Input bar to check your work.
Hit refresh to clear your work.
4. Write the equation of a line passing through points A(-3,-4) and B(-3,2). Enter your equation in the Input bar to check your work.
Hit refresh to clear your work.
5. Write the equation of a line passing through points A(-4,4) and B(3,4). Enter your equation in the Input bar to check your work.
Hit refresh to clear your work.
6. Equations of horizontal lines are always written in what form? Equations of vertical lines are always written in what form?