EXAMPLE 4 Write an equation given two points

EXAMPLE 5 Write a model using slope-intercept form Sports In the school year ending

EXAMPLE 5 Write a model using slope-intercept form SOLUTION STEP 1 Define the variables.

EXAMPLE 5 y Write a model using slope-intercept form = 2. 00 + 0.

for Examples 4 and 5 GUIDED PRACTICE Write an equation of the line that

GUIDED PRACTICE for Examples 4 and 5 You know the slope and a point

for Examples 4 and 5 GUIDED PRACTICE 7. (6, 1), (– 3, – 8)

for Examples 4 and 5 GUIDED PRACTICE 8. (– 1, 2), (10, 0) SOLUTION

GUIDED PRACTICE 9. for Examples 4 and 5 Sports In Example 5, the corresponding

GUIDED PRACTICE for Examples 4 and 5 SOLUTION STEP 1 Define the variables. Let

GUIDED PRACTICE m= y 2 – y 1 x 2 –x 1 for Examples

GUIDED PRACTICE y = for Examples 4 and 5 3. 42 + 0. 057

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EXAMPLE 4 Write an equation given two points Write an equation of the line that passes through (5, – 2) and (2, 10). SOLUTION The line passes through (x 1, y 1) = (5, – 2) and (x 2, y 2) = (2, 10). Find its slope. y 2 – y 1 m= x 2 –x 1 = 10 – (– 2) 2 – 5 = 12 – 3 =– 4

EXAMPLE 4 Write an equation given two points You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x 1, y 1) = (4, – 7). y 2 – y 1 = m(x – x 1) Use point-slope form. y – 10 = – 4(x – 2) Substitute for m, x 1, and y 1. y – 10 = – 4 x + 8 Distributive property y = – 4 x + 8 Write in slope-intercept form.

EXAMPLE 5 Write a model using slope-intercept form Sports In the school year ending in 1993, 2. 00 million females participated in U. S. high school sports. By 2003, the number had increased to 2. 86 million. Write a linear equation that models female sports participation.

EXAMPLE 5 Write a model using slope-intercept form SOLUTION STEP 1 Define the variables. Let x represent the time (in years) since 1993 and let y represent the number of participants (in millions). STEP 2 Identify the initial value and rate of change. The initial value is 2. 00. The rate of change is the slope m.

EXAMPLE 5 m= y 2 – y 1 x 2 –x 1 Write a model using slope-intercept form = 2. 86 – 2. 00 10 – 0 = 0. 86 10 Use (x 1, y 1) = (0, 2. 00) and (x 2, y 2) = (10, 2. 86). = 0. 086 STEP 3 Write a verbal model. Then write a linear equation.

EXAMPLE 5 y Write a model using slope-intercept form = 2. 00 + 0. 086 ANSWER In slope-intercept form, a linear model is y = 0. 086 x + 2. 00. x

for Examples 4 and 5 GUIDED PRACTICE Write an equation of the line that passes through the given points. 6. (– 2, 5), (4, – 7) SOLUTION The line passes through (x 1, y 1) = (– 2, 5) and (x 2, y 2) = (4, – 7). Find its slope. m= y 2 – y 1 x 2 –x 1 = – 7– 5 4 – (– 2) =– 2

GUIDED PRACTICE for Examples 4 and 5 You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x 1, y 1) = (4, – 7). y – y 1 = m(x – x 1) Use point-slope form. y – 7 = – 2(x – 4) Substitute for m, x 1, and y 1. y – 7 = – 2 (x + 4) Simplify y + 7 = – 2 x + 8 Distributive property y = – 2 x + 1 Write in slope-intercept form.

for Examples 4 and 5 GUIDED PRACTICE 7. (6, 1), (– 3, – 8) SOLUTION The line passes through (x 1, y 1) = (6, 1) and (x 2, y 2) = (– 3, – 8). Find its slope. m= y 2 – y 1 x 2 –x 1 = – 8– 1 – 3– 6 = – 9 =1

GUIDED PRACTICE for Examples 4 and 5 You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x 1, y 1) = (– 3, – 8). y – y 1 = m(x – x 1) y – (– 8)) = 1(x – (– 3)) Use point-slope form. Substitute for m, x, and y 1. y + 8 = 1 (x + 3) Simplify y+8= x+3 y =x– 5 Distributive property Write in slope-intercept form.

for Examples 4 and 5 GUIDED PRACTICE 8. (– 1, 2), (10, 0) SOLUTION The line passes through (x 1, y 1) = (– 1, 2) and (x 2, y 2) = (10, 0). Find its slope. m= y 2 – y 1 x 2 –x 1 = 0– 2 10– (– 1) = – 2 11

GUIDED PRACTICE for Examples 4 and 5 You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x 1, y 1) = (10, 0). y – y 1 = m(x – x 1) y – 0 = – 2 (x – 10) 11 2 y = – 11 (x – 10) 20 2 y = – 11 x + 11 20 2 = – 11 x + 11 Use point-slope form. Substitute for m, x, and y 1. Simplify Distributive property Write in slope-intercept form.

GUIDED PRACTICE 9. for Examples 4 and 5 Sports In Example 5, the corresponding data for males are 3. 42 million participants in 1993 and 3. 99 million participants in 2003. Write a linear equation that models male participation in U. S. high school sports.

GUIDED PRACTICE for Examples 4 and 5 SOLUTION STEP 1 Define the variables. Let x represent the time (in years) since 1993 and let y represent the number of participants (in millions). STEP 2 Identify the initial value and rate of change. The initial value is 3. 42. The rate of change is the slope m.

GUIDED PRACTICE m= y 2 – y 1 x 2 –x 1 for Examples 4 and 5 = 3. 99 – 3. 42 10 – 0 Use (x 1, y 1) = 3. 42 and (x 2, y 2) = 3. 99 = 0. 057 STEP 3 Write a verbal model. Then write a linear equation.

GUIDED PRACTICE y = for Examples 4 and 5 3. 42 + 0. 057 ANSWER In slope-intercept form, a linear model is y = 0. 057 x + 3. 42 x