Question

Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?

Answer 1

It has a y-intercept of 13.

Explanation:

no need for explanation because i got it right :)

Answer 2

The equation of a line that passes through two points
`(x_1, \, y_1)` and
`(x_2, \, y_2)` is given by

`(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)`

Give a line that passes through the points (6, 10) and (12, 7), the equation of the line is obtained as follows:

`(y-10)/(x-6) = (7-10)/(12-6)= (-3)/(6) =- (1)/(2) \\ \\ 2(y-10)=-(x-6) \\ \\ 2y-20=-x+6 \\ \\ 2y=-x+26 \\ \\ y=- (1)/(2) x+13`

The equation of a line in slope intercept form is given by

`y=mx+c`
where: m is the slope and c is the y-intercept.

Comparing this with the obtained equation of the line that passes through the points (6, 10) and (12, 7), we notice that the line has a slope of
`- (1)/(2)` and a y-intercept of 13.