Slope-Intercept Form of a Line - Activity A
Slope and y-intercept
In the slope-intercept form of the equation of a line, y = mx + b, m is the slope and b is the y-intercept.
1. Using the sliders, set m = 2 and b = 3 to graph the equation y = 2x + 3. (To quickly set a slider to a specific number, type the number in the box to the right of the slider, and then press ENTER.)
1. What is the value of m in this equation?
2. Click on the TABLE tab to see a table of solutions for this equation. What are two different solutions to y = 2x + 3? (Remember, a solution is an ordered pair.)
3. Using the two solutions you chose from the table, calculate the slope of the equation y = 2x + 3. Return to the CONTROLS tab and click Show triangle to make sure your answer is correct.
4. How does the slope that you calculated compare to the value of m in the equation?
2. What do you think the slope of the equation y = −3x + 1 is? Write down your answer and then use the Gizmo to graph y = −3x + 1. Click on Show triangle to see if your answer is correct.
3. Use the sliders to graph the equation y = 2x + 3.
1. What is the value of b in this equation?
2. What is the y-intercept of the graph of y = 2x + 3? Click on the TABLE tab and find the value of y when x = 0 to confirm your answer.
3. How does the y-intercept of the line compare to the value of b in the equation?
4. What do you think the y-intercept of the equation y = 0.5x − 2.5 is? Write down your answer and the use the Gizmo to graph y = 0.5x − 2.5. Click on the TABLE tab to check your answer.
Exploring Slope and y-intercept
1. Graph the equation y = 0 in the Gizmo. (Hint: This is the same as y = 0x + 0.)
1. What is the slope of this line? How would you describe this line?
2. Use the m slider to vary the slope. What happens to the line as you decrease the slope? What happens to the line as you increase the slope?
3. How would you describe the graph of the line when the slope is positive? How would you describe the graph when the slope is negative?
2. Graph the equation y = 0 in the Gizmo and use the slider to vary the value of b. How does the line change as you decrease the value of b? How does the line change as you increase the value of b?