Page 346 - Algebra 1

Application: Sales
Rachel is selling seashells. She sold 1 for $5 and 2 for $8. What will Rachel charge for 5 seashells if she keeps selling the seashells at the same price rate?
Understand
The ordered pair (1, 5) represents “1 shell for $5.” The ordered pair (2, 8) represents “2 shells for $8.” The slope represents the price rate, which is constant. Plan
Find the slope of the line.
Write an equation of the line that passes through (1, 5) and (2, 8).
Use the equation to find the value of y when x = 5.
Example
4
Math Reasoning
Predict Suppose Rachel sells some shells and receives $200. How many shells would she have sold if she had continued to sell the shells at the same price rate?
Solve
m = _y 2 - y 1 _x 2 - x 1
=8-5 2-1
=3
y-y1 =m(x-x1)
y - 5 = 3(x - 1) y - 5 = 3x - 3
y = 3x + 2
y = 3(5) + 2 y = 17
Write the slope formula.
Substitute (1, 5) for (x1, y1) and (2, 8) for (x2, y2).
Simplify.
Write the point-slope formula. Substitute (1, 5) for (x1, y1) and 3 for m. Distribute the 3.
Solve for y.
Substitute 5 for x.
Rachel will sell 5 seashells for $17.
Check
16 12
Graph y = 3x + 2.
The graph representing y = 3x + 2 goes through the
points (1, 5), (2, 8), and (5, 17).
8
(2, 8)
(5, 17)
4
O
(1, 5)
x
2
4
6
8
Lesson Practice
a. Graph a line that has a slope of 2 and passes through the point (5, 6). (Ex 1)
b. Graph a line that has a slope of 0 and passes through the point (-1, 1). (Ex 1)
c. Write the equation of a line that has a slope of 6 and passes through the
(Ex 2)
d. Write the equation of a line that passes through the points (2, -3) and
(Ex 3)
point (7, 9) in point-slope form.
(7, 4) in slope-intercept form.
y
Lesson 52 331