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12. – 3. 10 – (– 2). y 2 – y 1. =. m =. =. = – 4. x 2 – x 1. 2 – 5. 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

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12 – 3 10 – (– 2) y2 – y1 = m= = = – 4 x2 –x1 2 –5 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.

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 yrepresent 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.

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

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

– 7 – 5 y2 – y1 = m= = – 2 x2 –x1 4 –(– 2) for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 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.

for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 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.

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

for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 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.

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

2 – y – 0=(x – 10) 11 2 – y = (x – 10) 11 20 2 – y = x + 11 11 20 2 – x + = 11 11 for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 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. Substitute for m, x, and y1. Simplify Distributive property Write in slope-intercept form.

for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 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.

for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE SOLUTION STEP 1 Define the variables. Let x represent the time (in years) since 1993 and let yrepresent 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.

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

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