Question

What is the equation for a line that passes through W(2, -3) and is parallel to the line y=3x +5?

Doing a math review, stuck on some of these.

Answer 1

`"y = 3x - 9`

Explanation:

Given: `W(2, -3)` and the line `y = 3x + 5`

Parallel lines have the same slope. Find the slope of the given line. A line in the form of `y = mx + b` reveals the slope.

From the given line, `m = 3`

One way to find the parallel line through `(2, -3)` is to use the point-slope form of a line, `" "y - y_1 = m(x - x_1)`:

`y - -3 = 3 (x - 2)`

`y + 3 = 3x - 6`

Subtract the `3` from both sides: `" "y = 3x - 6 - 3`

Simplify: `" "y = 3x - 9`

A second way is to use `y = mx + b` and use the point `(2, -3)` to find the `y`-intercept `(0, b)`:

`-3 = 3(2) +b`

`-3 = 6 + b`

`-3 -6 = b`

`b = -9`

`y = 3x - 9`