Answer
(a) $y = -3x+1$
(b) $y = -5$
(c) $x = 2$
(d) $y = \frac{1}{2}x-6$
Work Step by Step
(a) We can find the y-intercept $b$:
$y = mx+b$
$y = -3x+b$
$(-5) = -3(2)+b$
$b = 6-5$
$b = 1$
The equation of the line is:
$y = -3x+1$
(b) If the line is parallel to the x-axis, then the slope is 0 and the value of $y$ is constant.
The equation of the line is:
$y = -5$
(c) If the line is parallel to the y-axis, then the value of $x$ is constant.
The equation of the line is:
$x = 2$
(d) We can find the slope of the given line:
$2x-4y = 3$
$4y = 2x-3$
$y = \frac{1}{2}x-\frac{3}{4}$
The slope of this line is $\frac{1}{2}$
We can find the y-intercept $b$:
$y = mx+b$
$(-5) = \frac{1}{2}(2)+b$
$b = -5-1$
$b = -6$
The equation of the line is:
$y = \frac{1}{2}x-6$
