Example 1 Write an Equation Given Slope and y-Intercept

Example 2 Write an Equation Given Two Points

Example 3Graph an Equation in Slope-Intercept Form

Example 4 Graph an Equation in Standard Form

Example 5 Write an Equation in Slope-Intercept Form

Write an equation of the line whose slope is and whose y-intercept is –6.

Slope-intercept form

Replace m with and b with –6.

Answer:

Write an equation of the line whose slope is 4and whose y-intercept is 3.

Answer:

Write an equation of the line shown in the graph.

Step 1 You know the coordinates of two points on the line. Find the slope. Let

Simplify.

The slope is 2.

Step 2 The line crosses the y-axis at (0, –3). So, the y-intercept is –3.

Step 3 Finally, write the equation.

Slope-intercept form

Replace m with 2 and b with –3.

Answer: The equation of the line is

Write an equation of the line shown in the graph.

Answer:

Graph

Step 1 The y-intercept is –7. So graph (0, –7).

Step 2 The slope is 0.5

or

From (0, –7), move up 1 unit and right 2 units. Draw a dot.

Step 3 Draw a line connecting the points.

y = 0.5x – 7

Graph

Answer:

Graph

Step 1 Solve for y to find the slope-intercept form.

Original equation

Subtract 5x from each side.

Simplify.

Divide each side by 4.

Divide each term in the numerator by 4.

Answer:

Step 2 The y-intercept of

is 2.

So graph (0, 2).

Step 3 The slope is

From (0, 2), move down 5 units and right 4 units. Draw a dot.

Step 4 Draw a line connecting the points.

5x + 4y = 8

Graph

Answer:

Health The ideal maximum heart rate for a 25-year-old who is exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute.

Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat.

Words The rate drops 3 beats per minute every

5 years, so the rate of change is

beats

per minute each year. The ideal maximum

heart rate for a 25-year-old is 117 beats

per minute.

Variables Let R = the ideal heart rate.Let a = years older than 25.

Equationideal rate

Ideal rate of years older for 25- rate equals change times than 25 plus year-old.

R a 117

Answer:

Graph the equation.

The graph passes through (0, 117) with a slope of

Answer:

Find the ideal maximum heart rate for a person exercising to burn fat who is 55 years old.

The age 55 is 30 years older than 25. So,

Ideal heart rate equation

Replace a with 30.

Simplify.

Answer: The ideal heart rate for a 55-year-old person is 99 beats per minute.

The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986.

a. Write a linear equation to find the average amount spent for any year since 1986.

Answer: where D is the amount of money spent in millions of dollars, and n is the number of years since 1986

The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986.

b. Graph the equation.

Answer:

The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986.

c. Find the amount spent by consumers in 1999.

Answer: $4.95 million