Question

find the equation of the line parallel to y=-5x+3 and passing through (4 3)

Answer 1

Parallel lines always have the same slope.

Information:
slope = -5
y-intercept = ?

We need the y-intercept!

3 = -5 (4) + b                    
3 = -20 + b                            Multiply.
23 = b                                   Add 20 to each side.

Now we have the y-intercept!

Information:
slope = -5
y-intercept = 23

Now, since we have the slope and y-intercept, we can form an equation!

y = -5x + 23

Answer: y = -5x + 23

Answer 2

So,

A parallel line will have the same slope as another parallel line.

We know this much of the parallel line:
y = -5x + b

To solve for b, all we have to do is substitute the given ordered pair for x and y, and then solve for b.
y = -5x + b
3 = -5(4) + b

Multiply.
3 = -20 + b

Add 20 to both sides.
23 = b

Now we have the complete equation.
y = -5x + 23