Question
Match the given information with the equation for the line.(4 points)
Put responses in the correct input to answer the question.
1. A line that contains the points (0, -2) and (4, 0).
2. A line that contains the point (0, -8) with a slope of 3/2
3. A line that contains the y-intercept (0, -2) and a slope of −3/4
4. A line that has a slope of 5/3 and a y-intercept of -4.
A. y = 3/2x - 8
B. 2y - x = -4
C. y = -3/4x - 2
D. -5x + 3y = -12
Put responses in the correct input to answer the question.
1. A line that contains the points (0, -2) and (4, 0).
2. A line that contains the point (0, -8) with a slope of 3/2
3. A line that contains the y-intercept (0, -2) and a slope of −3/4
4. A line that has a slope of 5/3 and a y-intercept of -4.
A. y = 3/2x - 8
B. 2y - x = -4
C. y = -3/4x - 2
D. -5x + 3y = -12
Answers
GPT-4o mini
Let's analyze each line and match them with the correct equation:
1. A line that contains the points (0, -2) and (4, 0).
- The slope can be calculated using \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2} \). The y-intercept is \(-2\). Using the slope-intercept form \(y = mx + b\), we can derive the equation:
\(y = \frac{1}{2}x - 2\). This does not match any given equations, so we'll check the others.
2. A line that contains the point (0, -8) with a slope of 3/2.
- The equation would be in the form \(y = mx + b\), where \(m = \frac{3}{2}\) and \(b = -8\):
\(y = \frac{3}{2}x - 8\). This matches with A.
3. A line that contains the y-intercept (0, -2) and a slope of −3/4.
- Similar to the previous, the equation would be:
\(y = -\frac{3}{4}x - 2\). This matches with C.
4. A line that has a slope of 5/3 and a y-intercept of -4.
- The equation would be:
\(y = \frac{5}{3}x - 4\). To compare with given equations, we rearrange D: \(-5x + 3y = -12\) into slope-intercept form:
\(3y = 5x - 12\) leads to \(y = \frac{5}{3}x - 4\). This matches with D.
Putting it all together:
1. (not found)
2. A: \(y = \frac{3}{2}x - 8\)
3. C: \(y = -\frac{3}{4}x - 2\)
4. D: \(-5x + 3y = -12\)
Final matches:
1: None
2: A
3: C
4: D
1. A line that contains the points (0, -2) and (4, 0).
- The slope can be calculated using \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2} \). The y-intercept is \(-2\). Using the slope-intercept form \(y = mx + b\), we can derive the equation:
\(y = \frac{1}{2}x - 2\). This does not match any given equations, so we'll check the others.
2. A line that contains the point (0, -8) with a slope of 3/2.
- The equation would be in the form \(y = mx + b\), where \(m = \frac{3}{2}\) and \(b = -8\):
\(y = \frac{3}{2}x - 8\). This matches with A.
3. A line that contains the y-intercept (0, -2) and a slope of −3/4.
- Similar to the previous, the equation would be:
\(y = -\frac{3}{4}x - 2\). This matches with C.
4. A line that has a slope of 5/3 and a y-intercept of -4.
- The equation would be:
\(y = \frac{5}{3}x - 4\). To compare with given equations, we rearrange D: \(-5x + 3y = -12\) into slope-intercept form:
\(3y = 5x - 12\) leads to \(y = \frac{5}{3}x - 4\). This matches with D.
Putting it all together:
1. (not found)
2. A: \(y = \frac{3}{2}x - 8\)
3. C: \(y = -\frac{3}{4}x - 2\)
4. D: \(-5x + 3y = -12\)
Final matches:
1: None
2: A
3: C
4: D