Graphing Using Slope-Intercept Form

Show your work for each problem.

1.
In the equation , what is the slope?
1. a)
2. b)
3. c)
4. d)
Answer:
In slope-intercept form , the slope is the number multiplied by . Here, .
2.
In the equation , what is the y-intercept?
1. a)
2. b)
3. c)
4. d)
Answer:
In slope-intercept form , the y-intercept is the constant term. Here, , so the line crosses the y-axis at .
3.
What is the y-intercept of the line ?
Answer: -8
In , the y-intercept is . The line crosses the y-axis at .
4.
What is the slope of the line ?
Answer: -5
In , the slope is . This means for every 1 unit increase in , decreases by 5.
5.
Which point does the line pass through on the y-axis?
1. a)
2. b)
3. c)
4. d)
Answer:
The y-intercept is , so the line crosses the y-axis at . Points on the y-axis always have .
6.
Graph by finding two points using the slope and y-intercept.
Answer: (0, -3) and (1, -1)
1. What is the y-intercept? (This is your first point) -3
2. Write the first point as coordinates: -3
3. What is the slope? 2
4. From , move up 2 and right 1. What is the y-coordinate of the new point? -1
7.
Convert to slope-intercept form and identify the slope.
Answer: -3
1. To isolate y, subtract from both sides. What do you get? y = -3x + 9
2. What is the slope? -3
3. What is the y-intercept? 9
8.
A line has slope and passes through . If you move 4 units right from this point, what is the new y-coordinate?
Answer: 1
With slope , moving 4 units right means moving 3 units up. Starting at : .
9.
Which equation represents a line that falls from left to right?
1. a)
2. b)
3. c)
4. d)
Answer:
has slope , which is negative, so the line falls from left to right. The others have positive or zero slopes.
10.
Graph . Find the coordinates of two points on this line.
Answer: (0, 4) and (2, 3)
1. What is the y-intercept? 4
2. The slope is . What does the numerator tell us? -1
3. What does the denominator tell us? 2
4. From , move down 1 and right 2. What is the new y-coordinate? 3
11.
Convert to slope-intercept form. What is the slope?
Answer: 2
. The slope is .
12.
A phone plan costs 25 euros per month plus 0.10 euros per text message. Write the equation in slope-intercept form and find the cost for 150 texts.
Answer: 40
1. What is the fixed monthly cost (y-intercept)? 25
2. What is the cost per text (slope)? 0.10
3. Write the equation in form : y = 0.10x + 25
4. Calculate for 150 texts: 40
13.
Two lines are parallel if they have the same slope. Which line is parallel to ?
1. a)
2. b)
3. c)
4. d)
Answer:
The original line has slope . Only has the same slope, so it's parallel. The y-intercepts are different, so the lines don't overlap.
14.
Convert to slope-intercept form and graph it by finding the y-intercept and one more point.
Answer: y = 2x + 4
1. Add to both sides. What do you get? 3y = 6x + 12
2. Divide everything by 3. What is the equation? y = 2x + 4
3. What is the slope? 2
4. What is the y-intercept? 4
5. From , use slope 2 to find another point. What is the y-coordinate at ? 6
15.
A line passes through and . What is the slope of this line?
Answer: 3
Slope . The equation would be .