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

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

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