Write the​ point-slope form of the line satisfying the given conditions. Then use the​ point-slope form of the equation to write the​ slope-intercept form of the equation.

Question

Write the​ point-slope form of the line satisfying the given conditions. Then use the​ point-slope form of the equation to write the​ slope-intercept form of the equation.

Slope=7​,

passing through

​(−4​,6​)

Answer 1

Use your point-slope form: y- y₁ = m (x - x₁) to substitute the given information.

y - 6 = 7(x - (-4))

Then simplify.

y - 6 = 7(x + 4)

Next, distribute the 7 into the parenthesis which will give you the point-slope form.

y - 6 = 7x + 28

In order to write it in slope-intercept form, add 6 to both sides.

y - 6 + 6 = 7x + 4 + 6

Then simplify to write the equation in slope-intercept form.

y = 7x + 10

Answer 2

The point-slope form looks like this:

y - y₁ = m (x - x₁) where (x₁,y₁) is a point on the line and m is the slope

Therefore for the first question:

m = 7

(x₁,y₁) = (-4,6)

Ans: y - 6 = 7 (x + 4) [Note: x - (-4) = x + 4]

For the second question:

The slope-intercept form looks like this:

y = mx + b

Since you have the point-slope form, all you have to do is solve for the slope-intercept form:

y - 6 = 7 (x + 4) [First, Isolate the left side so you only have y left]

y = 7(x+ 4) + 6 [Then solve for the right side until you have mx + b]

y = 7x + 28 + 6

y = 7x + 34

Ans: y = 7x + 34