Question

Write an equation of the line in point-slope form y-y_1=m(x-x_1) from the given point and slope.

(4,6); m=2

Answer 1

The equation in point-slope form is
`y-6=2(x-4)`.

Explanation:

We are given the slope and a coordinate pair of a line.

• Slope: 2
• Coordinate Pair (x, y): (4, 6)

Therefore, we can now label our coordinate pair and substitute our values into the formula. Our formula is:

`\displaystyle y-y_1=m(x-x_1)`

We can label our coordinate pairs with the
`(x_1, y_1)` labeling method.

Therefore, since our two coordinates are:

• x = 4
• y = 6

We can label 4 as x₁ and 6 as y₁.

Then, we are able to determine m, or our slope.

• m = 2

Now, let's set up our equation.

`\displaystyle y - y_1 = m(x - x_1)\\\\y - 6 = 2(x - 4)\\\\y - 6 = 2x - 8\\\\y = 2x - 2`

Therefore, our line is y = 2x - 2. However, the problem asks for it in point-slope form. So, this is exactly what we have in Step 2: y - 6 = 2(x - 4).