Question

the equation of the line a is given as y = -3/4 x -2. Suppose the line a is parallel to line b and lime t is perpendicular to line a. Point (0, 5) lines on both line b and line t.​

Answer 1

Answer: The equation for line b is $y = -\frac{3}{4}x + 5$

The equation for line t is $y= \frac{4}{3} x+5$

The attachment shows the original line in green, the parallel line b in red, and the perpendicular line t in blue.

Step-by-step explanation: Use slope intercept form, y = mx + b

The given coordinate, (0,5) is on the y-axis, so  5 will be the y-intercept of the equation. Keep the slope of the original equation and substitute the new value for "b"  

To write the equation for line t

Both lines share the y-intercept, (0,5) so the "b" term will be the same. The slope of a perpendicular line is the reciprocal of the original slope with the opposite sign.

So invert 3/4 to become 4/3 and change the negative sign to positive.

The resulting equation is y = 4x/3 + 5