The equation of ray pq is y=4x+3. the equation of ray vt is 2x+8y=16. rewrite the equation of ray vt in slope-intercdept form and determine if ray pq and ray vt are perpendicular

First, we transform the ray PQ in a slope-intercept form such as shown below:
y = 4x+3, where 4 is the slope of PQ
Then, we transform ray VT in slope-intercept as shown below:
2x + 8y =16
8y = 16 -2x
8y = -2x + 16
y = (-2x +16) /8
y = (-1/4)x + 2 , where the slope of VT is -1/4

Two lines which are perpendicular to each other has the second slope "inverse reciprocal" to the first slope. Therefore, they are perpendicular since the slope of VT is inverse reciprocal of slope QT.