1. Graphing Lines
Objectives
Find the slope of a line
Given an equation of a line, graph the line
Find the x-intercept and y-intercept of a line
Write the equation of a line from given information
Write the equation of a line parallel to a given line
Write the equation of a line perpendicular to a given line

2. Why study lines?
Many equations in science and business are equations of lines
In the business world, being able to interpret graphs and pie charts are a necessity

3. Characteristics of a line
How steep? Slope
Rising or falling? (positive or negative slopes)
What points lie on the line? (y-intercepts, x-intercepts, other points)

4. Rising or falling
Rising or falling – By convention, graphs in business and science are read from left to right
Negative slope – falling
Positive slope – rising

5. Undefined slope (vertical line)
Special cases of slope
Undefined slope (vertical line)
Zero slope (horizontal line)

6. Calculating the slope, given two points
The slope measures the steepness of the line; how fast does the vertical change with each run? y x
(3, 6)
rise = = 5 units
(1, 1)
run = = 2 units

7. Equation of a line in slope-intercept form
Look at the graph of y = 2x – 1 .
The y – value of the point where the line crosses the y-axis is ___.
- 1
This value is called the ____________ of the line.
y - intercept
Most linear equations can be written in the form __________.
y = mx + b
This form is called the ___________________.
slope – intercept form
y = 2x – 1 y x 5 -2 1 3 -3 2 -1 4
y = mx + b
slope
y - intercept
y = 2x – 1
(0, -1)

8. Graphing a line Graph 2x + y = 3
1) Rewrite the equation in slope – intercept form by solving for y. 2)
y = –2x + 3 y x 5 -2 1 3 -3 2 -1 4
3) Identify and graph the y-intercept.
(0, 3)
4) Follow the slope to a second point on the line.
(1, 1)
5) Draw the line between the two points.

9. Facts about graphs y = mx + b x intercept: y = 0 y intercept: x = 0y x 5 -2 1 3 -3 2 -1 4
y = mx + b
slope
y - intercept
x intercept: y = 0
y intercept: x = 0
Parallel lines have equal slopes (same steepness)
Perpendicular lines have slopes
that are negative reciprocals of each other

10. Finding the x-intercept and y-intercept; p. 167 TXTBK Ex 2
6x + 3y = 12
(Standard form)
y intercept:
Let x = 0
0 + 3y = 12
y = 4
(0,4) is the y-intercept
x intercept:
Let y = 0
6x + 0 = 12
x = 2
(2,0) is the x-intercept

11. Finding the equation of a line, given the slope ,one point
Slope-intercept formula
y = mx + b
4 = 3(-1) + b (Substitute)
4 = -3 + b
7 = b
y = 3x + 7
p. 168 TXTBK Ex. 4
Line through (-1, 4) with slope 3
Point-slope formula
y – y1 = m(x – x1)
y – 4 = 3(x – –1)
y – 4 = 3(x + 1)

12. Finding the equation of a line, given two points
Step 1. Find the slope of the line with the two points.
Step 2. Use one of the methods on the previous slide to find the equation of the line with a slope and one point.

13. Finding the equation of a parallel line
P. 175 TxtBk Ex 3
Write an equation of a line parallel to
y = -4x + 3 and containing (1, -2)
Parallel line so slopes are the same
y = mx + b
y = -4x + b
-2 = -4(1) + b (Substitution)
-2 = -4 + b
b = 2
y = -4x + 2

14. Finding the equation of a perpendicular line
Find the equation of the line that contains (-3, 7) and is perpendicular to y = -3x + 5
Perpendicular so slope is the negative reciprocal = 1/3
y = mx + b
7 = 1/3 (-3) + b (Substitute x = -3, y = 7)
7 = -1 + b
8 = b
y = 1/3 x + 8

15. Vertical lines x is always 2 on the vertical line soy x 5 -2 1 3 -3 2 -1 4
x is always 2 on the vertical line so
x = 2 is the equation;
slope is undefined since rise/run = rise/0 ;
cannot divide by 0

16. Horizontal lines y is always 3 on the horizontal line soy x 5 -2 1 3 -3 2 -1 4
y is always 3 on the horizontal line so
y = 3 is the equation;
Slope = 0 since slope = rise/run and rise = 0