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