Question

A line passes through `(4 ,9 )` and `(1 ,6 )`. A second line passes through `(3 ,7 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

(0,4)

Explanation:

First of all, both of the lines are parallel to each other, meaning they have the same slope

To find the slope, we use the slope formula:

`(y_2-y_1)/(x_2-x_1)`

Plug in the numbers from the points of the 2 lines, and find the slope of both lines

`(9-6)/(4-1) = 3/3 = 1`

The 1 is the slope of both of the lines, as parallel lines have the same slope.

Now, we can use the point-slope formula to get the slope-intercept equation of the second line

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

Plug in the numbers, and get the new formula

`y-7=1(x-3)`
`y-7=x-3`
`y=x+4`

Now, we can get a second point for the second line: the y-intercept. To find the y-intercept, plug in 0 for the x value of the equation, and simplify. The resulting point found should be your new answer:

`(0,4)`