Answer
a. $y=-\frac{5}{2}x+4$
b. $y=\frac{2}{5}x+4$
Work Step by Step
a.
Rewrite the equation in slope-intercept form $y=mx+b$:
$$2y=-5x+3$$
$$y=-\frac{5}{2}x+\frac{3}{2}$$
Thus, the slope of the equation is $-\frac{5}{2}$.
Recall that parallel lines have the same slopes. Then, using the point-slope form $y-y_1=m(x-x_1)$:
$$y-4=-\frac{5}{2}(x-0)$$
$$y-4=-\frac{5}{2}x$$
$$y=-\frac{5}{2}x+4$$
b.
Recall that the relation of perpendicular lines is:
$$m_1m_2=-1$$
$$-\frac{5}{2}m_2=-1$$
$$m_2=\frac{2}{5}$$
Using the point-slope form:
$$y-4=\frac{2}{5}(x-0)$$
$$y-4=\frac{2}{5}x$$
$$y=\frac{2}{5}x+4$$
