ALGEBRA 5.75.7 Point-Slope Form

LEARNING TARGETS

Language Goal Students will be able to explain how to

graph a line and write a linear equation using point-slope form.

Math Goal Students will be able to write a linear

equation given two points.Essential Question Why is it important to have different

forms to graph a line?

WARM-UP

HOMEWORK CHECK

HOMEWORK CHECK

EXAMPLE 1: USING SLOPE AND A POINT TO GRAPH

Steps are the same as if you were given a y-intercept

Step 1: Plot the given point

Step 2: Use the slope to move from the given point to the next point.

Step 3: Connect the points.

EXAMPLE 1: USING SLOPE AND A POINT TO GRAPH

A. Slope = ; (3, -2) B. Slope = 3; (1, 1)

EXAMPLE 1: USING SLOPE AND A POINT TO GRAPH

C. Slope = ; (3, 2) D. Slope = -1; (2, -2)

POINT-SLOPE FORMULA

is the given point

m = slope,

EXAMPLE 2: WRITING LINEAR EQUATIONS IN POINT-SLOPE FORM

Write an equation in point-slope form for the line with the given slope that contains the given point.

A. Slope = (-3, 0) B. Slope = -7; (4, 2)

EXAMPLE 2: WRITING LINEAR EQUATIONS IN POINT-SLOPE FORM

Write an equation in point-slope form for the line with the given slope that contains the given point.

C. Slope = 0 (-2, -3) D. Slope = 2; (, 1)

EXAMPLE 3: WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT

FORM

Slope Intercept Form: y = mx + b

Yesterday: Step 1: Find the y – intercept by...

Plugging in the slope and the ordered pair. Solve for b.

Step 2: Write the equation using the slope and b.

Today:Step 1: Write the equation in point-slope form.Step 2: Write the equation in slope-intercept form by solving for y.

EXAMPLE 3: WRITING LINEAR EQUATIONS IN SLOPE-INTERCEPT

FORM

Write an equation in slope-intercept form for the line with the given slope and contains the point.

A. Slope = -4 (-1, -2) Yesterday’s method Today’s method y = mx + b

EXAMPLE 3: WRITING LINEAR EQUATIONS INS SLOPE-INTERCEPT

FORM

Write an equation in slope-intercept form for the line with the given slope and contains the point.

B. Slope = C. Slope = 3; (-1, 4)

EXAMPLE 4: USING TWO POINTS TO WRITE AN EQUATION.

Step 1: Find the slope. Step 2: Substitute the slope and one of the

points into the point-slope form Step 3: Write the equations in slope-

intercept form by solving for y.

EXAMPLE 4: USING TWO POINTS TO WRITE AN EQUATION.

Write an equation in slope-intercept form for the line through the two points.

A. (1, -4) and (3, 2) B. (4, -7) and (0, 5)

EXAMPLE 4: USING TWO POINTS TO WRITE AN EQUATION.

Write an equation in slope-intercept form for the line through the two points.

C. (1, -2) and (3, 10) D. (6, 3) and (0, -1)

EXAMPLE 5: WORD PROBLEMS

The cost to place an ad in a newspaper for one week is a linear function of the number of lines in the ad. The costs for 3, 5, and 10 lines are shown. Write an equation in slope-intercept form that represents the function. Then find the cost of an ad that is 18 lines long.

Lines 3 5 10

Cost $ 13.50

18.50

31

EXAMPLE 5: WORD PROBLEMS

At a different newspaper, the costs to place an ad for one week are shown. Write an equation in slope-intercept form that represents this linear function. Then find the cost of an ad that is 21 lines long.Lines 3 5 10

Cost $ 12.75

17.25

28.50

SUMMING IT UP!

Use the two points in the

formula to find the slope. Then use the slope and one of the points to write the equation in

point-slope form.

If the slope is m and y –intercept

is b, then the equation is y = mx + b

Use the slope and the point to

write the equation in

point-slope form.

LESSON QUIZ