Writing Linear Equations

Show your work for each problem.

1.
What is the equation of a line with slope and y-intercept ?
1. a)
2. b)
3. c)
4. d)
Answer:
Substituting and into gives .
2.
A line has slope and passes through the origin. What is the equation? Write in the form .
Answer: y = 4x
Since the line passes through the origin, . With , the equation is or simply .
3.
Which equation represents a line with slope and y-intercept ?
1. a)
2. b)
3. c)
4. d)
Answer:
With slope and y-intercept , the equation is .
4.
Calculate the slope of the line through and .
Answer: 3
5.
Write the equation of the line with slope passing through the point .
Answer: y = 4x + 3
1. Write the point-slope form: . What do you get when you substitute? y - 11 = 4(x - 2)
2. Distribute the 4 on the right side. What is ? 4x - 8
3. Add 11 to both sides to solve for . What is the final equation? y = 4x + 3
6.
What is the slope of the line through the points and ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Write the equation of the line through and in slope-intercept form.
Answer: y = 3x + 4
1. Calculate the slope using . What is ? 3
2. One point is . What is the y-intercept ? 4
3. Write the equation . y = 3x + 4
8.
A gym charges 20 euros per month plus 5 euros per class. Write the equation for total monthly cost in terms of classes . (Write as C = ...)
Answer: C = 5c + 20
Rate = 5 euros/class (slope), base = 20 euros (y-intercept). So .
9.
A table shows: when , ; when , . What is the equation?
1. a)
2. b)
3. c)
4. d)
Answer:
Slope: . Using : . So .
10.
Write the equation of the line through and .
Answer: y = 3x - 5
1. Calculate the slope 3
2. Use point-slope form with : . Expand the right side. 3x - 6
3. Add 1 to both sides. What is the final equation? y = 3x - 5
11.
Write the equation of the line with slope passing through . Give your answer in slope-intercept form.
Answer: y = -2x + 11
12.
Write the equation of the line through and .
Answer: y = -2x + 3
1. Calculate (change in y) -8
2. Calculate (change in x) 4
3. What is the slope ? -2
4. Using point and slope , find the y-intercept . 3
5. Write the final equation. y = -2x + 3
13.
A car rental costs 30 euros per day plus 0.20 euros per kilometer. Which equation represents the total cost for days and kilometers?
1. a)
2. b)
3. c)
4. d)
Answer:
Daily cost = 30 euros days. Kilometer cost = 0.20 euros km. Total: .
14.
A water tank has 200 liters and drains at 15 liters per minute. Write the equation for the amount of water after minutes, and find when the tank will be empty.
Answer: 13.33
1. What is the rate of change (slope)? Remember: draining means negative! -15
2. What is the starting amount (y-intercept)? 200
3. Write the equation W = ? -15t + 200
4. Set and solve for . What is (round to 2 decimals)? 13.33
15.
Line passes through and . What is the y-intercept of line ?
Answer: 2
Slope: . Using : .
16.
Write the equation of a horizontal line passing through .
Answer: y = 5
1. What is the slope of a horizontal line? 0
2. For a horizontal line, y is always the same. What value does y always equal? 5
3. Write the equation. y = 5