1. Linear Functions

2. Review of Formulas Formula for Slope Standard Form
*where A>0 and A, B, C are integers
Slope-intercept Form
Point-Slope Form

3. Find the slope of a line through points (3, 4) and (-1, 6).

4. Change into standard form.

5. Change into slope-intercept form and identify the slope and y-intercept.

6. Write an equation for the line that passes through (-2, 5) and (1, 7):
Find the slope:
Use point-slope form:

7. x-intercepts and y-intercepts
The intercept is the point(s) where the graph crosses the axis.
To find an intercept, set the other variable equal to zero.

8. Horizontal Lines Slope is zero. Equation form is y = #.
Write an equation of a line and graph it with zero slope and y-intercept of -2.
y = -2
Write an equation of a line and graph it that passes through (2, 4) and (-3, 4).
y = 4

9. Vertical Lines Slope is undefined. Equation form is x = #.
Write an equation of a line and graph it with undefined slope and passes through (1, 0).
x = 1
Write an equation of a line that passes through (3, 5) and (3, -2).
x = 3

10. Graphing Lines graph a line. Using x and y intercepts:
*You need at least 2 points to
graph a line.
Using x and y intercepts:
Find the x and y intercepts
Plot the points
Draw your line

11. Graph using x and y intercepts
2x – 3y = -12
x-intercept
2x = -12
x = -6
(-6, 0)
y-intercept
-3y = -12
y = 4
(0, 4)

12. Graph using x and y intercepts
6x + 9y = 18
x-intercept
6x = 18
x = 3
(3, 0)
y-intercept
9y = 18
y = 2
(0, 2)

13. Graphing Lines Using slope-intercept form y = mx + b:
Change the equation to y = mx + b.
Plot the y-intercept.
Use the numerator of the slope to count the
corresponding number of spaces up/down.
Use the denominator of the slope to count the corresponding number of spaces left/right.
Draw your line.

14. Graph using slope-intercept form y = -4x + 1:
y-intercept
(0, 1)
Slope
m = -4 = -4 1

15. Graph using slope-intercept form
3x - 4y = 8
y = 3x - 2 4
y-intercept
(0, -2)
Slope
m = 3 4

16. Section 2.3 – Linear Functions and Slope-Intercept Form
Problem 3:
Write the equation in slope-intercept form. What are the slope and y-intercept?
5x – 4y = 16
-3/4x+1/2y = -1
3x + 2y = 18
-7x – 5y = 35

17. Parallel Lines **Parallel lines have the same slopes.
Find the slope of the original line.
Use that slope to graph your new line and to write the equation of your new line.

18. Graph a line parallel to the given line and through point (0, -1):
Slope = 3 5

19. Write the equation of a line parallel to
2x – 4y = 8 and containing (-1, 4):
– 4y = - 2x + 8
y = 1x - 2 2
Slope = 1
y - 4 = 1(x + 1) 2

20. Perpendicular Lines **Perpendicular lines have the
opposite reciprocal slopes.
Find the slope of the original line.
Change the sign and invert the
numerator and denominator
of the slope.
Use that slope to graph your new
line and to write the equation
of your new line.

21. Graph a line perpendicular to the given line and through point (1, 0):
Slope =-3 4
Perpendicular
Slope= 4 3

22. Write the equation of a line perpendicular to
y = -2x + 3 and containing (3, 7):
Original Slope= -2
Perpendicular
Slope = 1 2
y - 7 = 1(x - 3) 2

23. Write the equation of a line perpendicular to
3x – 4y = 8 and containing (-1, 4):
-4y = -3x + 8
y - 4 = -4(x + 1) 3
Slope= 3 4
Perpendicular
Slope = -4 3