Write an equation given two points EXAMPLE 4 Write an equation of the line that passes through (5,...
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Write an equation given two points EXAMPLE 4 te an equation of the line that passes through (5, (2, 10). SOLUTION e line passes through (x 1 , y 1 ) = (5,– 2) and , y 2 ) = (2, 10). Find its slope. y 2 – y 1 m = x 2 –x 1 10 – (– 2) = 2 – 5 12 – 3 = = – 4
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Transcript of Write an equation given two points EXAMPLE 4 Write an equation of the line that passes through (5,...
Write an equation given two points
EXAMPLE 4
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 – y1m =x2 –x1
10 – (– 2) =
2 – 5
12– 3= = – 4
Write an equation given two points
EXAMPLE 4
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
Write in slope-intercept form.y = – 4x + 8
Write a model using slope-intercept formEXAMPLE 5
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.
Write a model using slope-intercept form
EXAMPLE 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 2.00. The rate of change is the slope m.
Write a model using slope-intercept form
EXAMPLE 5
y2 – y1m =x2 –x1
2.86 – 2.00 = 10 – 0
0.86 = 10
= 0.086
Use (x1, y1) = (0, 2.00)
and (x2, y2) = (10, 2.86).
STEP 3
Write a verbal model. Then write a linear equation.
Write a model using slope-intercept form
EXAMPLE 5
y = 2.00 + 0.086 x
ANSWER
In slope-intercept form, a linear model is y = 0.086x + 2.00.
GUIDED PRACTICE for Examples 4 and 5GUIDED 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.
y2 – y1m =x2 –x1
– 7 – 5 =
4 – (– 2)= – 2
GUIDED PRACTICE for Examples 4 and 5GUIDED 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.
y – 7 = – 2 (x + 4)
Distributive property
Write in slope-intercept form.y = – 2x + 1
y + 7 = – 2x + 8
Simplify
GUIDED PRACTICE for Examples 4 and 5GUIDED PRACTICE
7. (6, 1), (–3, –8)
SOLUTION
The line passes through (x1, y1) = (6, 1) and (x2, y2) = (–3, –8). Find its slope.
y2 – y1m =x2 –x1
– 8 – 1 =
– 3 – 6
– 9– 9= = 1
GUIDED PRACTICE for Examples 4 and 5GUIDED 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.
y – y1 = m(x – x1) Use point-slope form.
Substitute for m, x, and y1.
Distributive property
Write in slope-intercept form.y = x – 5
Choose (x1, y1) = (– 3, – 8).
Simplify
y – (– 8)) = 1(x – (– 3))
y + 8 = 1 (x + 3)
y + 8 = x + 3
GUIDED PRACTICE for Examples 4 and 5GUIDED PRACTICE
8. (–1, 2), (10, 0)
SOLUTION
The line passes through (x1, y1) = (– 1, 2) and (x2, y2) = (10, 0). Find its slope.
y2 – y1m =x2 –x1
0 – 2 =
10– (– 1)
211= –
GUIDED PRACTICE for Examples 4 and 5GUIDED 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.
y – y1 = m(x – x1) Use point-slope form.
Substitute for m, x, and y1.
Distributive property
Write in slope-intercept form.
Choose (x1, y1) = (10, 0).
Simplify
y – 0 = (x – 10) 211
–
y = (x – 10)211
–
y = 211
– x + 2011
211
– x + 2011=
GUIDED PRACTICE for Examples 4 and 5GUIDED 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.
GUIDED PRACTICE for Examples 4 and 5GUIDED PRACTICE
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 for Examples 4 and 5GUIDED PRACTICE
y2 – y1m =x2 –x1
3.99 – 3.42 = 10 – 0
= 0.057
Use (x1, y1) = 3.42
and (x2, y2) = 3.99
STEP 3
Write a verbal model. Then write a linear equation.
GUIDED PRACTICE for Examples 4 and 5GUIDED PRACTICE
y = 3.42 + 0.057 x
ANSWER
In slope-intercept form, a linear model is y = 0.057x + 3.42
