COLLEGE ALGEBRA: AN INVESTIGATIVE APPROACH

by

S. Kastberg & T. Barron


ALGEBRAIC FORMS OF LINEAR FUNCTIONS


Please type your answers to the questions in the lesson in the text boxes below. Please type all your answers in complete sentences. After you have entered all your answers please be sure to click on the submit button at the end of the lesson.


y = mx + b

Consider the graph below.

1. What is the slope of the line graphed?

2. What is the y-intercept of the line graphed?

Another name for the y-intercept is b.

3. Of the following equations, which do you think is the equation of the line graphed?

y = -2x - 4

y = 2x - 4

y = 2x + 4

y = x - 4

y = x + 4

Please explain why you chose the equation you did.

 

4. Using what you learned in question three and lesson 2, find the equations of the red and green lines on the following graph.

The red line has equation

The green line has equation

5. Find the equation of a line whose slope is -2 and whose y-intercept is 4.

6. Find the equation of a line whose slope is and whose y-intercept is -1.

7. Find the x-intercept of the line in question 6.

8. The equation that we used in the previous less and in questions one through seven is called the slope-intercept form of a line. The slope-intercept form of a line is great to use when you know or can find the and the .

y - y1 = m(x - x1)

9. Suppose I want to find the equation of line whose slope is -2 and that passes through the point (-1,3).

Click HERE to graph the line described.

10. Can we easily determine the equation of the line in slope-intercept form? (y = mx + b)?

11. Sometimes slope-intercept form is not the easiest form to use in finding the equation of a line. Since we have the slope and a point, let's look at the equation for slope that you developed in yesterday's lesson.

Assuming m = -2, x1 = -1, and y1 = 3 what equation results from subsituting these values into .

12. Solve the equation from question 11 for y2.

13. Keeping in mind what you learned in question 12, what do you think the slope-intercept form of the line whose slope is -2 and that passes through the point (-1,3) is?

14. Graph a line whose slope is and that passes through the point (-2,5).

Click HERE to graph the line described.

15. Find the equation of the line your graphed.

16. Find the x-intercept of the line you graphed.

PARALLEL LINES

17. Find the equation for a line whose slope is -2 and that passes through the point (4,5).

18. Find the equation for a lne whose slope is -2 and that passes through the point (-4,5).

Graph the lines whose equations you found in problems 17 and 18. Click HERE to graph the lines.

19. These two lines are .

20. Parallel lines have slopes.

PERPENDICULAR LINES

21. Find the equation for the line whose slope is and that passes through the point (-4,5).

Graph the lines whose equation you found in problems 17 and 21. Click HERE to graph the lines.

22. These two lines are.

23. Find the slopes of the red and green lines on the graph below.

The slope of the red line is and the slope of the green line is .

24. These two lines are

25. Perpendicular lines have slopes.


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