A line with a slope of -2 passes through the point (4, 7). Write an equation for this line in point-slope form.y – 7 = (x – )

Question

y – 7 =_____  (x – ____)

What are the Blanks?

Answer 1

Gene does a good job of showing you one way of doing it, but the simpler way to find what you are looking for is...

y - y₁ = m(x - x₁) with (x₁,y₁) being your given point.

y - 7 = -2(x - 4)

Answer 2

There will be two stages to this solution.

1) Find an equation for the line.

2) Put it in the form asked for.

y=mx+b They've given us the value of m. It's the slope: m=-2

We can use the known point (4, 7) for values of x and y that must make the equation true.

Substitute the known values for m, x and y, then solve for b, the only remaining variable.

x=4, y=7, m=-2

7 = (-2)(4) + b

7 = -8 + b

7+8 = b

b = 15

Now write the equation:

y = -2x + 15

Stage 1 is complete.

We need the equation to look like this y-7 = (___)(x-___)

The equation we have found has just "y" on the left side. All we have to do do is subtract 7 from BOTH sides of the equation to get started.

y = -2x + 15

y-7 = -2x + 15 - 7 The left side is now correct and both sides are still equal.

Simplify:

y-7 = -2x + 8

Factor -2 out of the two terms on the right.

y-7 = -2(x-4)

BINGO!

There's a "-2" before the x-term, and a "-4" after the x.