Let's match each given line description with the appropriate equation:
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A line that has a slope of \(\frac{5}{3}\) and a y-intercept of -4.
The equation of a line in slope-intercept form is \(y = mx + b\).
Here, \(m = \frac{5}{3}\) and \(b = -4\).
Therefore, the equation is:
\(y = \frac{5}{3}x - 4\).
(This equation is not in the provided options.) -
A line that contains the points (0,-2) and (4,0).
First, we can find the slope using the points: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}. \] Since it goes through (0, -2), we can use the point-slope formula to write the equation: \[ y + 2 = \frac{1}{2}(x - 0) \implies y = \frac{1}{2}x - 2. \] Checking the options, let's re-examine:
The equation \(2y - x = -4\) can be rearranged: \[ 2y = x - 4 \implies y = \frac{1}{2}x - 2. \] So, this matches. -
A line that contains the point (0,-8) with a slope of \(\frac{3}{2}\).
The equation in slope-intercept form will be: \[ y = \frac{3}{2}x - 8. \] This matches with the option:
\(y = \frac{3}{2}x - 8\). -
A line that contains the y-intercept (0,-2) and a slope of -\(\frac{3}{4}\).
The equation in slope-intercept form will be: \[ y = -\frac{3}{4}x - 2. \] This matches with the equation \(y = -\frac{3}{4}x - 2\).
Summary of Matches:
- A line that has a slope of \(\frac{5}{3}\) and a y-intercept of -4: No match in the options.
- A line that contains the points (0,-2) and (4,0): \(2y - x = -4\)
- A line that contains the point (0,-8) with a slope of \(\frac{3}{2}\): \(y = \frac{3}{2}x - 8\)
- A line that contains the y-intercept (0,-2) and a slope of -\(\frac{3}{4}\): \(y = -\frac{3}{4}x - 2\)
1 answer