Lesson 5-4 Point-Slope Form Sept. 22, 2014. Daily Learning Target I will write and graph linear...
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Transcript of Lesson 5-4 Point-Slope Form Sept. 22, 2014. Daily Learning Target I will write and graph linear...
Lesson 5-4Point-Slope Form
Sept. 22, 2014
Daily Learning Target
• I will write and graph linear equations using point-slope form.
What is it?
y – y1 = m(x – x1)
m = slope(x1, y1) = a point the line goes through.
Here is how it works!!• Given a point (x1, y1) on a line and the
line’s slope m, you can use the definition of slope to derive point-slope form.
• Definition of slope (m) = • Let (x, y) be any point on the line.
Substitute for (x, y) for (x2, y2).• = m
How it works cont.
• = m• Multiply both sides by = m() point-slope formm = slope(x1, y1) = a point the line goes through.
Example 1
• A line passes through (-3, 6) and has slope -5. What is an equation of the line in point slope form?
**Remember: = m()
= -5()
You Try It
• A line passes through (8, -4) and has slope . What is an equation in point-slope for of the line?
y + 4 = (x – 8)
Example 2
• What is the graphof the equationy – 1 = (x – 2)What is the slope?
What is the pointit passes through?
You Try
• What is the graph of the equation:a. y + 7 = - (x – 4)b. y – 1 = -3(x + 2)c. y – 2 = (x – 3)
Example 3
• What is an equation of the line from the coordinate plane?
Steps to think about:• Think --You need the slope m, so start with
the slope formula.– Use the given points to find the slope– Use point-slope form– Use either point for (x1, y1).
You Try
• Use the same procedure as the example to write the equation for a graph where the line goes through points (-3, 4) and (1, 1).
y – 1 = - (x – 1)
Example 4
• The table shows the altitude of a hot-air balloon during its linear descent. What equation in point-slope form. What does it look like in slope-intercept form?
• PSF: y – 640 = -2.5(x – 10)
• SIF: y = -2.5x + 665
Time, x (s) Altitude, y (m)
10 640
30 590
70 490
90 440
You Try
• The table shows the number of gallons of water, y, in a tank after x hours. The relationship is linear. What is an equation in point-slope forms that models that data. What does the slope
represent? PSF: y – 3320 = 1250(x – 2);The rate at which water is being added to the tank.
Time, x (h) Water, y (gal)
2 3320
3 4570
5 7070
8 10,820
Homework
• Workbook:• Page 151 problems 1, 3, 4, 6, 7, 8, 10, 11, 13• Page 153 problems 1-6 ALL