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 (x1, y1) = (5,– 2) and (x2, y2) = (2, 10). Find its slope. y2 – y1 m = x2 –x1 10 – (– 2) = 2 – 5 12 – 3 = – 4

Write an equation given two points 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 (x1, y1) = (4, – 7). y2 – y1 = m(x – x1) Use point-slope form. y – 10 = – 4(x – 2) Substitute for m, x1, and y1. y – 10 = – 4x + 8 Distributive property y = – 4x + 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.

Write a model using slope-intercept form EXAMPLE 5 Write a model using slope-intercept form y2 – y1 m = x2 –x1 2.86 – 2.00 = 10 – 0 Use (x1, y1) = (0, 2.00) and (x2, y2) = (10, 2.86). 0.86 = 10 = 0.086 STEP 3 Write a verbal model. Then write a linear equation.

EXAMPLE 5 Write a model using slope-intercept form y = 2.00 + 0.086 x ANSWER In slope-intercept form, a linear model is y = 0.086x + 2.00.

GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5 Write an equation of the line that passes through the given points. 6. (– 2, 5), (4, – 7) SOLUTION The line passes through (x1, y1) = (– 2, 5) and (x2, y2) = (4, – 7). Find its slope. y2 – y1 m = x2 –x1 – 7 – 5 = 4 – (– 2) = – 2

GUIDED PRACTICE 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 (x1, y1) = (4, – 7). y – y1 = m(x – x1) Use point-slope form. y – 7 = – 2(x – 4) Substitute for m, x1, and y1. Simplify y – 7 = – 2 (x + 4) y + 7 = – 2x + 8 Distributive property y = – 2x + 1 Write in slope-intercept form.

GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5 7. (6, 1), (–3, –8) SOLUTION The line passes through (x1, y1) = (6, 1) and (x2, y2) = (–3, –8). Find its slope. y2 – y1 m = x2 –x1 – 8 – 1 = – 3 – 6 – 9 = 1

GUIDED PRACTICE 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 (x1, y1) = (– 3, – 8). y – y1 = m(x – x1) Use point-slope form. y – (– 8)) = 1(x – (– 3)) Substitute for m, x, and y1. y + 8 = 1 (x + 3) Simplify y + 8 = x + 3 Distributive property y = x – 5 Write in slope-intercept form.

GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5 8. (–1, 2), (10, 0) SOLUTION The line passes through (x1, y1) = (– 1, 2) and (x2, y2) = (10, 0). Find its slope. y2 – y1 m = x2 –x1 0 – 2 = 10– (– 1) 2 11 –

GUIDED PRACTICE 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 (x1, y1) = (10, 0). y – y1 = m(x – x1) Use point-slope form. y – 0 = (x – 10) 2 11 – Substitute for m, x, and y1. y = (x – 10) 2 11 – Simplify y = 2 11 – x + 20 Distributive property 2 11 – x + 20 = Write in slope-intercept form.

GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5 9. 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 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.

Write a verbal model. Then write a linear equation. GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5 y2 – y1 m = x2 –x1 3.99 – 3.42 = 10 – 0 Use (x1, y1) = 3.42 and (x2, y2) = 3.99 = 0.057 STEP 3 Write a verbal model. Then write a linear equation.

GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5 y = 3.42 + 0.057 x ANSWER In slope-intercept form, a linear model is y = 0.057x + 3.42