M098
Carson Elementary and Intermediate Algebra 3e
Section 4.4
Objectives
1.
2.
3.
4.
Compare lines with different slopes.
Graph equations in slope-intercept form.
Use slope-intercept form to write the equation of a line (Do NOT stress!)
Find the slope of a line given two points on the line.
Vocabulary
Slope
The ratio of the vertical change between any two points on a line and the horizontal
change between the points. (Rise over run).
Slope-intercept
form
y = mx + b
Prior Knowledge
New Concepts
1.
Positive slope (m > 0): the graph is a line that slants uphill from left to right.
2.
Negative slope (m< 0): the graph is a line that slants downhill from left to right.
3.
Graph a line using a point and a slope:
Plot the point and then use the slope to “rise and run” to find a second point
Example 1:
Graph the line through (-4, 3) with a slope of -2/3.
Plot (-4, 3)
Rise -2 (down) and run 3
(right)
4.
Graph equations in slope-intercept form: y = mx + b.
Find the slope and y-intercept from the equation.
Example 2:
y = -3x + 5
y-intercept: (0, 5)
m = -3 = -3/1
V. Zabrocki 2011
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M098
Carson Elementary and Intermediate Algebra 3e
Example 3:
Section 4.4
2x – y = 5
Rewrite in y = mx + b form
-y = -2x + 5
y = 2x – 5
y-intercept = (0,-5)
m=2
Example 4:
4x – 3y = 12
Rewrite in y = mx + b form.
-3y = -4x + 12
4
y  x4
3
y-intercept = (0, -4)
4
m 
3
****Compare the slope that you found in Examples 3 and 4 to the original equation that was
written in standard form. When an equation is written in standard form (Ax + By = C), the slope
can be found by
m
A
. In Example 3, A = 2 and B = -1 so m = - 2/-1 = 2. In Example 4,
B
A = 4 and B = -3 so m = - 4/-3 = 4/3. This shortcut is not mentioned in the text.
5. Use slope-intercept form to write the equation of a line. (Do not dwell on this limited case.)
If the slope and y-intercept of a line is known, it is very easy to write the equation of the line. Just
substitute the slope for m and the y-coordinate of the y-intercept for b in y = mx + b.
Unfortunately, most of the time the point we know is NOT the y-intercept so this does us little good.
y  y1
vertical distance
 2
horizontal distance
x 2  x1
The notation used for general points in this section is sometimes confusing to students.
6. Find the slope of a line given two points: m 
(x1, y1) and (x2, y2) represent two different points. x1 is the x-coordinate of the first point. x2 is the xcoordinate of the second point. Likewise, y1 is the y-coordinate of the first point; y2 the y-coordinate
of the second point.
Example 5:
V. Zabrocki 2011
Find the slope of the line through
5
3
(6, 2) and (3, 7).
m  
(-4, -6) and (2, -3)
m 
(-2, -8) and (4, -8)
m=0
horizontal line
(-3, 2) and (-3, 5)
m = undefined
vertical line
1
2
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