Question

How do you write an equation of a line that passes through the point (3, 2) and is parallel to the line y=3x-4?

Answer 1

`y - 2= 3(x - 3)` or `y = 3x - 7`

Explanation:

For a line to be parallel to another line, by definition it must have the same slope. Because the equation is in the slope-intercept form we can use the slope of the line.

The slope-intercept form of a linear equation is:

`color(red)(y = mx + b)`
Where `m` is the slope and `b` is the y-intercept value.

Therefore, for the given equation the slope is `3`.

Now we can use the point slope formula to determine the equation for the parallel line.

The point-slope formula states: `color(red)((y - y_1) = m(x - x_1))`
Where `m` is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope from the given line and the given point gives:

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

Transforming this to the slope-intercept form by solving for `y` gives:

`y - 2 = 3x - 9`

`y - 2 + 2 = 3x - 9 + 2`

`y = 3x - 7`