Determine the equation of the following lines

parallel to y=3x-2 and passes through(1,4)

perpendicular to y=-3/4x+5 and passes through(-3,-6)

perpendicular to 5x+2y-4=0 and has the same y-intercept as 2x+3y-15=0

Hint: When an equation is parallel to another, they have the same slope and when it's perpendicular, the slope is inverted.

Let's start with the first one. Since it's parallel, we're keeping the slope which is 3. Now, you just plug in the coordinate pair and solve for the y-intercept.

4 = 3(1) + b
4 = 3 + b
b = 1

Therefore the equation would be y = 3x + 1.

Next one is perpendicular so we invert the slope to give it a negative-reciprocal, making the slope 4/3. Now, you plug in and solve.

-6 = 4/3(-3) + b
-6 = -8 + b
b = 2

Therefore, the equation is y = 4/3x + 2

Next, you need to put the equations into y=mx+b

Equation for slope:
5x + 2y -4 = 0
2y = -5x + 4
y = -5/2x + 2

Since the slope is perpendicular the slope would be 2/5.

Equation for y-intercept:
2x + 3y - 15 = 0
3y = -2x + 15
y = -2/3x + 5

Since it has the same y-intercept, it stays as a 5.

The final equation would be y = 2/5x + 5.