Writing Equations in Slope-Intercept Form

Write an equation of a line that passes through (2, –3)

with slope

Step 1 The line has slope To find the y-intercept,

replace m with and (x, y) with (2, –3) in the

slope-intercept form. Then, solve for b.

Write an Equation Given Slope and One Point

Slope-intercept form

Replace m with ,y with –3,and x with 2.

Multiply.

Subtract 1 from each side.

Simplify.

Write an Equation Given Slope and One Point

Step 2 Write the slope-intercept form using

Slope-intercept form

Replace m with and b with –4.

Answer: The equation is

Write an Equation Given Slope and One Point

Write an equation of a line that passes through (1, 4) and has a slope of –3.

Answer:

Write an Equation Given Slope and One Point

Writing Equations in Slope-Intercept Form

If you are not given the slope but you know two points on the line, find the slope first then choose one of the points to find the y-intercept.

Multiple-Choice Test Item

The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function?

A B

C D

x y

–3 –4

–2 –8

Read the Test Item The table represents the ordered pairs (–3, –4) and (–2, –8).

Write an Equation Given Two Points

Solve the Test Item Step 1 Find the slope of the line containing the points.

Let and.

Slope formula

Simplify.

Write an Equation Given Two Points

Step 2 You know the slope and two points. Choose one point and find the y-intercept. In this case, we chose (–3, –4).

Slope-intercept form

Replace m with –4,x with –3, and y with –4.

Multiply.

Subtract 12 from each side.

Simplify.

Write an Equation Given Two Points

Step 3 Write the slope-intercept form using

Answer: The equation is The answer is D.

Slope-intercept form

Replace m with –4 and b with –16.

Write an Equation Given Two Points

x y

–1 3

2 6

Multiple-Choice Test Item

The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function?

A B

C D

Answer: B

Write an Equation Given Two Points

Writing Equations in Slope-Intercept Form

You may need to rewrite the information as two points then find the slope and y-intercept.

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).

Write an Equation to Solve a Problem

Solve Find the slope.

Letand .

Slope formula

Simplify.

Write an Equation to Solve a Problem

Choose (5, 1.76) and find the y-intercept of the line.

Slope-intercept form

Replace m with0.37, x with 5,and y with 1.76.

Multiply.

Subtract 1.85 from each side.

Simplify.

Write an Equation to Solve a Problem

Slope-intercept form

Write the slope-intercept form usingand

Replace m with 0.37 and b with –0.09.

Answer: The equation is

Write an Equation to Solve a Problem

Examine Check your result by substituting the coordinates of the point not chosen, (6, 2.13), into the equation.

Original equation

Replace y with 2.13 and x with 6.

Multiply.

Simplify.

Write an Equation to Solve a Problem

The average cost of a college textbook in 1997 was $57.65. In 2000, the average cost was $68.15. Write a linear equation to estimate the average cost of a textbook in any given year since 1997. Let x represent years since 1997.

Answer:

Write an Equation to Solve a Problem

Writing Equations in Slope-Intercept Form

Writing Equations in Slope-Intercept Form

Linear extrapolation is when you use a linear equation to predict values that are beyond the range of the data.

Be cautious when making a prediction using just two given points.

The model may be approximately correct but still give inaccurate predictions.

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.

Linear Extrapolation

Answer: If gas increases at the same rate, a gallon of gasoline will cost $2.50 in July. 3000 gallons at this price is $7500, so they will have to add $500 to their budget.

A student is starting college in 2004 and has saved$400 to use for textbooks. Use the prediction equation where x is the years since 1997 and y is the average cost of a college textbook, to determine whether they will have enough money for 5 textbooks.

Answer: If the cost of textbooks increases at the same rate, the average cost will be $82.15 in 2004. Five textbooks at this price is $410.75, so he will not have enough money.

Linear Extrapolation