1. Writing Equations in Slope-Intercept Form
Lesson 5-4
Writing Equations in Slope-Intercept Form

2. Click the mouse button or press the Space Bar to display the answers.
Transparency 4

3. Transparency 4a

4. Objectives
Write an equation of a line given the slope and one point on a line
Write an equation of a line given two points on a line

5. Vocabulary
Linear extrapolation – the use of a linear equation to predict values that are outside the data range

6. x-y Coordinate Plane Point Plotting Quadrants II I III IV
up 7
left 4
right 5
III IV
down 8
(x, y) (-4, 7) (5, -8)
x – left or right
y – up or down

7. Example 1
Write an equation of a line that passes through (2, –3) with slope ½
Step 1 The line has slope ½ To find the y-intercept, replace m with ½ and (x, y) with (2, –3) in the slope-intercept form. Then, solve for b.
Slope-intercept form
Replace m with ½ , y with –3, and x with 2.
Multiply.
Subtract 1 from each side.
Simplify.

8. Example 1 cont Step 2 Write the slope-intercept form using
Replace m with and b with –4.
Answer: The equation is
Using your calculator to graph it and the CALC menu to verify that it passes through (2, –3).

9. Example 2
Economy In 2000, the cost of many items increased because of the increase in the cost of petroleum. In Chicago, a gallon of self-serve regular gasoline cost $1.76 in May and $2.13 in June. Write a linear equation to predict the cost of gasoline in any month in 2000, using 1 to represent January.
Explore You know the cost of regular gasoline in May and June.
Plan Let x represent the month and y represent the cost of gasoline that month. Write an equation of the line that passes through (5, 1.76) and (6, 2.13).

10. Example 2 cont
Solve Find the slope.
Slope formula
Let and .
Simplify.

11. Example 2 cont Choose (5, 1.76) and find the y-intercept of the line.
Slope-intercept form
Replace m with 0.37, x with 5, and y with 1.76.
Multiply.
Subtract 1.85 from each side.
Simplify.
Replace m with 0.37 and b with –0.09.
Answer: The equation is

12. Example 3
Economy The Yellow Cab Company budgeted $7000 for the July gasoline supply. On average, they use 3000 gallons of gasoline per month. Use the prediction equation where x represents the month and y represents the cost of one gallon of gasoline, to determine if they will have to add to their budget. Explain.
Original equation
Replace x with 7.
Simplify.
Answer: If gas increases at the same rate, a gallon of gasoline will cost $2.50 in July gallons at this price is $7500, so they will have to add $500 to their budget.

13. Summary & Homework Summary: Homework:
To write an equation given the slope and one point, substitute the values of m, x, and y into the slope-intercept form and solve for b. Then write the slope-intercept form using the values of m and b
To write an equation given two points, find the slope. Then follow the steps above
Homework:
Pg even
No graph