**(1) Linear Equation for JD Drew's Hits:**
Given: 22 games, 32 hits; 36 games, 60 hits.
Let x represent the number of games and y represent the number of hits.
Two points can be formed: (22, 32) and (36, 60).
Slope (m) = (60 - 32) / (36 - 22) = 28 / 14 = 2
Using the point-slope form and one of the points, let's use (22, 32):
y - 32 = 2(x - 22)
y = 2x - 44 + 32
y = 2x - 12
**Linear equation**: y = 2x - 12
**(2) Equation Through Point (4, -7) and (0, 5):**
Slope (m) = (5 - (-7)) / (0 - 4) = 12 / -4 = -3
Now use point (0, 5) for the y-intercept (b), which is already given.
**Linear equation**: y = -3x + 5
**(3) Equation for Cost of Fabric:**
Given: 2 yards cost $13; 5 yards cost $32.50.
Let x represent yards and y represent cost.
Points: (2, 13) and (5, 32.50).
Slope (m) = (32.5 - 13) / (5 - 2) = 19.5 / 3 = 6.5
Using y-intercept form:
y = 6.5x + b
Use point (2, 13) to find b:
13 = 6.5(2) + b
b = 13 - 13 = 0
**Linear equation**: y = 6.5x
**(4) Equation Through Point (6, 3) and (0, -1):**
Slope (m) = (3 - (-1)) / (6 - 0) = 4 / 6 = 2/3
Using the y-intercept -1, given by point (0, -1).
**Linear equation**: y = (2/3)x - 1
**(5) Equation Through Point (-2, 2) and (2, -2):**
Slope (m) = (-2 - 2) / (2 - (-2)) = -4 / 4 = -1
Since the line crosses the y-axis at 0 (due to symmetry of points), y-intercept (b) = 0.
**Linear equation**: y = -1x
**(6) Equation Through Point (0, -4) and (1, -6):**
Slope (m) = (-6 - (-4)) / (1 - 0) = -2 / 1 = -2
Using the y-intercept -4, given by point (0, -4).
**Linear equation**: y = -2x - 4
**(7) Equation for Oven Temperature:**
Given: 1 minute, 125ºF; 4 minutes, 290ºF.
Let x represent minutes and y represent temperature (ºF).
Points: (1, 125) and (4, 290).
Slope (m) = (290 - 125) / (4 - 1) = 165 / 3 = 55
Using the point-slope form and point (1, 125):
y - 125 = 55(x - 1)
y = 55x - 55 + 125
**Linear equation**: y = 55x + 70
**(8) Equation Through Point (-3, 1) and (0, 10):**
Slope (m) = (10 - 1) / (0 - (-3)) = 9 / 3 = 3
Using the y-intercept 10, given by point (0, 10).
**Linear equation**: y = 3x + 10
**(9) Equation Through Point (7, 8) and (6, 9):**
Slope (m) = (9 - 8) / (6 - 7) = 1 / -1 = -1
Using point-slope form with point (7, 8):
y - 8 = -1(x - 7)
y = -1x + 7 + 8
**Linear equation**: y = -x + 15
**(10) Key Club Fundraiser:**
Given: 60 people, $500; 80 people, $1500.
Let x represent people and y represent money made.
Points: (60, 500) and (80, 1500).
Slope (m) = (1500 - 500) / (80 - 60) = 1000 / 20 = 50
Using y = mx + b and point (60, 500) to find b:
500 = 50(60) + b
b = 500 - 3000
b = -2500
**Linear equation**: y = 50x - 2500
**(11) Equation Through Point (7, 8) and (-7, 6):**
Slope (m) = (6 - 8) / (-7 - 7) = -2 / -14 = 1/7
Using point-slope form with point (7, 8):
y - 8 = (1/7)(x - 7)
y = (1/7)x - 1 + 8
**Linear equation**: y = (1/7)x + 7
**(12) Equation Through Point (2, 7) and (-4, 4):**
Slope (m) = (4 - 7) / (-4 - 2) = -3 / -6 = 1/2
Using the point-slope form with point (2, 7):
y - 7 = (1/2)(x - 2)
y = (1/2)x - 1 + 7
**Linear equation**: y = (1/2)x + 6
**(13) Equation for Bluegill Fish Length:**
Given: 1 year old, 3 inches; 4 years old, 6 inches.
Let x represent years and y represent length (inches).
Points: (1, 3) and (4, 6).
Slope (m) = (6 - 3) / (4 - 1) = 3 / 3 = 1
Using the point-slope form and point (1, 3):
y - 3 = 1(x - 1)
y = x + 2
**Linear equation**: y = x + 2
**(14) Equation Through Point (4, -1) and (-8, -10):**
Slope (m) = (-10 - (-1)) / (-8 - 4) = -9 / -12 = 3/4
Using point-slope form and point (4, -1):
y - (-1) = (3/4)(x - 4)
y + 1 = (3/4)x - 3
**Linear equation**: y = (3/4)x - 4
(1) After 22 games, JD Drew had 32 hits. After 36 games he had 60 hits.
Write a linear equation in slope-intercept form to describe the situation.
(2) Write an equation in slope-intercept form for the line that passes through the two points.
(4, -7) and (0, 5)
(3) Two yards of fabric costs $13 and 5 yards of fabric costs $32.50.
Write an equation in slope-intercept form to describe the cost, y, for each yard x.
(4) Write an equation in slope-intercept form for the line that passes through the two points.
(6, 3) and (0, -1)
(5) Write an equation in slope-intercept form for the line that passes through the two points.
(-2, 2) and (2, -2)
(6) Write an equation in slope-intercept form for the line that passes through the two points.
(0, -4) and (1, -6)
(7) Megan is baking cookies. The oven temperature is 125ºF after one minute and 290ºF after four minutes.
Write an equation in slope-intercept form that describes the oven temperature.
(8) Write an equation in slope-intercept form for the line that passes through the two points.
(-3, 1) and (0, 10)
(9) Write an equation in slope-intercept form for the line that passes through the two points.
(7, 8) and (6, 9)
(10) The Key Club is hosting a banquet as a fundraiser. If 60 people attend, they make $500. If 80 people attend, they make $1500.
Write an equation in slope-intercept form to describe the situation.
(11) Write an equation in slope-intercept form for the line that passes through the two points.
(7, 8) and (-7, 6)
(12) Write an equation in slope-intercept form for the line that passes through the two points.
(2, 7) and (-4, 4)
(13) A one year old bluegill fish is 3 inches long and a four year old bluegill fish is 6 inches long.
Write an equation in slope-intercept form for the length, y, of a bluegill fish after x years.
(14) Write an equation in slope-intercept form for the line that passes through the two points.
(4, -1) and (-8, -10)
1 answer
1 answer