Let's analyze each line and match them with the correct equation:
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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.
- 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:
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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.
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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.
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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:
- (not found)
- A: \(y = \frac{3}{2}x - 8\)
- C: \(y = -\frac{3}{4}x - 2\)
- D: \(-5x + 3y = -12\)
Final matches: 1: None 2: A 3: C 4: D