Graphing Using Intercepts

Show your work for each problem.

1.
What is the x-intercept of a line?
1. a)The slope of the line
2. b)The point where the line crosses the x-axis
3. c)The midpoint of the line
4. d)The point where the line crosses the y-axis
Answer: The point where the line crosses the x-axis
The x-intercept is the point where the line crosses the x-axis. At this point, the y-coordinate is always 0.
2.
To find the y-intercept, which variable do you set equal to zero?
1. a)
2. b)Both and
3. c)
4. d)Neither
Answer:
To find the y-intercept, set and solve for . The y-intercept is where the line crosses the y-axis, and every point on the y-axis has an x-coordinate of 0.
3.
Find the x-intercept of . Write only the x-coordinate.
Answer: 5
Setting : , so . The x-intercept is .
4.
Find the y-intercept of . Write only the y-coordinate.
Answer: 5
Setting : , so . The y-intercept is .
5.
Which ordered pair represents an x-intercept?
1. a)
2. b)
3. c)
4. d)
Answer:
is an x-intercept because it lies on the x-axis (y = 0). would be a y-intercept, and is both an x-intercept and y-intercept (the origin).
6.
Find the x-intercept of . Write only the x-coordinate.
Answer: 6
Setting : , so , and . The x-intercept is .
7.
Find the y-intercept of . Write only the y-coordinate.
Answer: 4
Setting : , so , and . The y-intercept is .
8.
Find the x-intercept and y-intercept of .
Answer: x-intercept: (2, 0), y-intercept: (0, -4)
1. To find the x-intercept, set y = 0. What equation do you get? 4x = 8
2. Solve for x. What is the x-intercept (x-coordinate only)? 2
3. To find the y-intercept, set x = 0. What equation do you get? -2y = 8
4. Solve for y. What is the y-intercept (y-coordinate only)? -4
9.
A line has x-intercept and y-intercept . Through which quadrants does this line pass?
1. a)Quadrants I, III, and IV
2. b)Quadrants I and III
3. c)Quadrants I, II, and III
4. d)Quadrants II and IV
Answer: Quadrants I, III, and IV
The line goes from in Quadrant IV, crosses the x-axis at , continues into Quadrant I, and extends through Quadrant III when extended left. It passes through Quadrants I, III, and IV.
10.
Graph using intercepts. Find both intercepts first.
Answer: x-intercept: (2, 0), y-intercept: (0, -6)
1. Set y = 0 to find the x-intercept. What is 3x when y = 0? 3x = 6
2. Solve for x: 2
3. Set x = 0 to find the y-intercept. What is -y when x = 0? -y = 6
4. Solve for y: -6
11.
Find the y-intercept of . Write only the y-coordinate.
Answer: 3
Setting : , so , and . The y-intercept is .
12.
Graph using intercepts and verify by finding a third point.
Answer: x-intercept: (2, 0), y-intercept: (0, 5), verification point: (4, -5)
1. Find the x-intercept (x-coordinate only): 2
2. Find the y-intercept (y-coordinate only): 5
3. To verify, let x = 4. Substitute into the equation and solve for y: -5
4. Does the point (4, -5) lie on the line connecting (2, 0) and (0, 5)? yes
13.
The equation passes through the origin. What is special about its intercepts?
1. a)It has no y-intercept
2. b)Both intercepts are at (0, 0)
3. c)It has no x-intercept
4. d)The intercepts are at (3, 0) and (0, 3)
Answer: Both intercepts are at (0, 0)
For : When , (y-intercept at origin). When , gives (x-intercept at origin). Both intercepts are at , which is why you need another method (like using the slope) to graph lines through the origin.
14.
A company's profit equation is , where is the number of items sold and is profit in euros. Find the break-even point using intercepts.
Answer: 20 items
1. At break-even, profit P equals what value? 0
2. Set P = 0 in the equation. What do you get? 0 = 25x - 500
3. Add 500 to both sides: 500 = 25x
4. Divide by 25. How many items must be sold? 20
15.
Find the x-intercept of . Write only the x-coordinate.
Answer: 3
Setting : . The x-intercept is . This equation is in intercept form, where the denominators are the intercepts!
16.
The line has an x-intercept at . Find the value of .
Answer: 2
1. At the x-intercept (4, 0), what are the values of x and y? x = 4, y = 0
2. Substitute these values into the equation : 4a + 0 = 8
3. Simplify: 4a = 8
4. Solve for a: 2