Slope-Intercept Form (y = mx + b)

Show your work for each problem.

1.
What is the slope of ?
Answer: 4
In , the slope m is the number multiplied by x. Here, .
2.
What is the y-intercept of ?
Answer: -5
In , the y-intercept b is the constant. Here, (note the negative!).
3.
A line passes through and has slope . What is the equation in slope-intercept form? Write as y=mx+b
Answer: y=-3x+7
The point is on the y-axis, so . With slope , the equation is .
4.
If a line has slope , starting at , what is the y-value when ?
Answer: 5
Equation: . When : .
5.
A line passes through and . What is the slope?
Answer: 3
6.
Which line has a positive slope?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the slope is , which is positive. The other equations have negative or zero slopes.
7.
Where does the line cross the y-axis?
1. a)
2. b)
3. c)
4. d)
Answer:
The y-intercept is , which means the line crosses the y-axis at .
8.
Convert to slope-intercept form.
1. a)
2. b)
3. c)
4. d)
Answer:
→ . Subtract 3x from both sides.
9.
Which lines are parallel?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
Parallel lines have the same slope. Both and have slope .
10.
A line passes through and . What is its equation?
1. a)
2. b)
3. c)
4. d)
Answer:
Slope: . Y-intercept: . Equation: .
11.
A phone plan costs 25 dollars per month plus 2 dollars per GB. What equation represents the total cost y for x GB?
1. a)
2. b)
3. c)
4. d)
Answer:
Cost per GB (2) is the slope (rate of change). Monthly fee (25) is the y-intercept (starting cost). So .
12.
Identify the slope and y-intercept of
Answer: m=5, b=-2
1. What is the coefficient of x (the slope)? 5
2. What is the constant (the y-intercept)? -2
13.
Graph . Find the y-intercept and one more point.
Answer: (0,3) and (1,5)
1. What is the y-intercept? This gives you point (0, ?) 3
2. The slope is 2. From (0, 3), go up 2 and right 1. What is the y-coordinate of the new point? 5
3. What is the x-coordinate of that new point? 1
14.
Convert to slope-intercept form.
Answer: y=-2x+10
1. Subtract 2x from both sides. What is on the left side now? y
2. What is on the right side? -2x+10
3. What is the slope? -2
15.
Find the equation of a line with slope passing through .
Answer: y=3x-4
1. The point is on the y-axis. What is the y-intercept (b)? -4
2. We know and . Write the equation in the form y=mx+b (no spaces): y=3x-4
16.
Find the slope of the line passing through and .
Answer: 3
1. Calculate the rise (change in y): 9
2. Calculate the run (change in x): 3
3. Calculate slope: rise/run = 3
17.
A line passes through and . Write the equation in slope-intercept form.
Answer: y=2x+1
1. Calculate the slope: 2
2. Use point to find b. If , what is b? 1
3. Write the final equation (no spaces): y=2x+1
18.
A gym charges 50 dollars to join plus 30 dollars monthly. How much will you pay after 6 months?
Answer: 230
1. What is the slope (monthly cost)? 30
2. What is the y-intercept (signup fee)? 50
3. Calculate total for 6 months: 230