Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept...
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![Page 1: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/1.jpg)
![Page 2: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/2.jpg)
Find the slope-intercept form, given a linear equation
Graph the line described the slope-intercept form
What is the relationship between the slopes of parallel lines?
What is the relationship between the slopes of perpendicular lines?
![Page 3: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/3.jpg)
Recall the point-intercept form of linear equation.
y – y1
----- = m x – x1
y – y1 = m (x – x1)
E.g., y – 1 = 3(x – 2)
![Page 4: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/4.jpg)
• y – y1 = m(x – x1)
• Suppose (x1, y1) = (0, b)Then
• y – y1 = m(x – x1)y – b = mxy = mx + b
m = slopeb = y-intercept
![Page 5: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/5.jpg)
• y = ½ x + 3
m = ½b = 3
• y = 2 x – 5
m = 2b = -5
![Page 6: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/6.jpg)
• Find the slope and the y-intercept of the line.
a) 2x + 5y = 3 5y = -2x + 3 y = (-2/5)x + 3/5 m = -2/5 b = 3/5
b) 3x – 4y = 9
![Page 7: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/7.jpg)
Suppose a line has a slope of 5 and passes through (-2, 9). Write the slope-intercept form of the equation for the line.
Solutiony = mx + b9 = 5(-2) + b19 = b
y = 5x + 19
![Page 8: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/8.jpg)
Suppose that a line passes through the following 2 points: (-3, 4), (5, -8).Write the slope-intercept form of the equation of the line.
Solution:m = (-8 – 4)/(5 – (-3)) = -12/8 = -3/2y = mx + b4 = (-3/2)(-3) + b4 = 9/2 + bb = -1/2
y = (-3/2)x – 1/2
![Page 9: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/9.jpg)
y = (4/3)x – 2
m = 4/3b = -2
![Page 10: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/10.jpg)
Find the slope and the y-intercept of the line: 2(x – 3) = –3(y + 5). Graph the equation.
Solution 2x – 6 = -3y – 15
3y = -2x – 9y = (-2/3)x – 3
m = -2/3b = -3
![Page 11: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/11.jpg)
Show that the lines represented by 4x + 8y = 16 and x = 6 – 2y are parallel.
Two lines are parallel if their slopes are equal4x + 8y = 16 x = 6 – 2y8y = -4x + 16 2y = -x + 6y = -(1/2)x = 2 y = (-1/2) + 3
![Page 12: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/12.jpg)
2 and -1/2 are negative reciprocals of each other.
So are 3/4 and -4/3. What is the negative reciprocal of 3/5?
If two lines are perpendicular to each other, their slopes are negative reciprocals
If the slopes of two lines are negative reciprocals, the lines are perpendicular.
![Page 13: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/13.jpg)
![Page 14: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/14.jpg)
Write an equation of the line passing through (–3, 2) and parallel to the line y = 8x – 5.
Solution:Solve for b, in y = mx + b
![Page 15: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/15.jpg)
A company buys a $12,500 computer with an estimated life of 6 years. The computer can then be sold as scrap for an estimated salvage value of $500. If y represents the value of the computer after x years of use and y and x are related by the equation of a line,
a. Find an equation of the line and graph it.b. Find the value of the computer after 2 years.c. Find the economic meaning of the y-intercept of the
line.d. Find the economic meaning of the slope of the line.
![Page 16: Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept form What is the relationship between the slopes.](https://reader030.fdocuments.us/reader030/viewer/2022032709/56649ee05503460f94bf04aa/html5/thumbnails/16.jpg)