Slope
Find the slope of each line.
a) m = 2
b) m = -1/2
c) undefined
d) zero
Write an equation in slope-intercept form of a line whose slope is -8 and y-intercept is 5.
y = -8x + 5
Graph x = -5.
Undefined slope, going through the x-axis at -5
Write an inequality to represent the graph.
y > 3x + 6
Solve for y.
9y - 18x = 45
9y - 18x = 45
9y = 45 + 18x
y = 5 + 2x
Find the slope of the line that goes through the points (-12, 18) and (-12, 20).
Undefined
Write the equation of the line graphed in simplest slope-intercept form.
y = -3/5x - 9
Graph the equation y = -2/3x - 4
Graph starts at -4 on y-axis, then down 2 right 3.
Is the point (3, 4) in the solution set of the inequality:
y > -5x + 13
4 > -5(3) + 13
4 > -2
Yes it is.
Is the point (-5, -30) on the line y = 6x - 9?
-30 = 6(-5) - 9
-30 = -39
No
Find the slope of the line that goes through the points (-8, 13) and (25, -20).
-33/33 = -1
Write an equation in point-slope form of a line that passes through the points (-4, 13) and (-7, 23).
23 - 13 = 10
-7 + 4 = -3
m = -10/3
y - 13 = -10/3(x + 4)
OR
y - 23 = -10/3(x + 7)
An electrician charges an insurance fee and an hourly rate. The amount of money an electrician charges is represented by e(h) = 450 + 65.50h. Explain each part of the function: e(h), 450, 65.50, and h.
e(h) = total
450 = insurance fee
65.50 = hourly rate
h = number of hours worked
Graph 5x - y <= -2
-y <= -2 + 5x
y >= 2 - 5x
Start at 2 on y-axis, then down 5 right 1.
Shade away from (0,0)
Is the points (-4, -15) in the solution set of
2y > 3x - 18
2(-15) > 3(-4) - 18
-30 > -30
No.
A line goes through the points (-7, 18) and (-4, k) and has a slope of -9. What is the value of k?
k = -9
Use point-slope form to write an equation in slope-intercept form of a line that goes through the point (4, -6) and has a slope of -2.
y + 6 = -2(x - 4)
y + 6 = -2x + 8
y = -2x + 2
The temperature outside is falling at a steady rate of 3 degrees per hour. It started at 72 degrees.
Write an equation to represent the temperature, y, after x hours.
Then using your equation, determine the temperature have 8 hours.
Using your equation, how many hours have passed when the temperature is 54 degrees?
y = -3x + 72
y = -3(8) + 72
y = 48
48 degrees
54 = -3x + 72
-18 = -3x
6 = x
6 hours
John pays $5 per pound of apples and $15 per pie crust. If he can spend at most $45, write an inequality to represent this situation. Use x for pounds and y for pie crusts.
Graph the inequality and state one point in the solution set.
5x + 15y <= 45
15y <= 45 - 5x
y <= 3 - 1/3x
Start at 3 on y-axis, down 1 right 3.
Shade toward (0,0)
Multiple points in solution set.
Use point-slope form to write an equation in slope-intercept form of a line that goes through the points (-5, 9) and (-12, -19).
-19 - 9 = 28
-12 + 5 = -7
m = -4
y - 9 = -4(x + 5)
y - 9 = -4x - 20
y = -4x - 11
A line goes through the points (k, -21) and (-8, 35) and has a slope of 4. What is the value of k?
k = -22
Use point-slope form to write an equation in slope-intercept form of a line that goes through the points (-6, 9) and (-12, -19).
-19 - 9 = 28
-12 + 6 = -6
m = -14/3
y - 9 = -14/3(x + 6)
y - 9 = -14/3x - 28
y = -14/3x - 19
Kelly is saving money. She deposits $350 into a savings account and then puts $150 in the account each month.
Write an equation to represent Kelly's total amount, y, after m months.
Graph your equation.
How much money will Kelly have after 2 years?
y = 150x + 350
Graph starts at 350 on the y-axis, then up 150 right 1.
y = 150(24) + 350
y = 3950
$3,950
Andrew buys lollipops for $1 each and drinks for $3 each for his friends. He has $27 to spend. Write an inequality using x for lollipops and y for drinks.
Graph your inequality.
Can he buy 7 lollipops and 7 drinks for his friends? Use your inequality to determine your answer.
x + 3y <= 27
3y <= 27 - x
y <= 9 - 1/3x
Start at 9 on y-axis, down 1 right 3.
Shade toward (0,0)
7 + 3(7) <= 27
7 + 21 <= 27
28 <= 27
No he can't buy 7 lollipops and 7 drinks.
A commuter purchases a $500 fare card. Each ride on the subway costs $2.50. Write an equation to represent the number of rides, r, the commuter goes on and the total amount on his card, c.
Using your equation, determine how much money he would have after 30 rides.
c = -2.50r + 500
c = -2.50(30) + 500
c = $425