Question

A line passes through the points (1, -6) and (4, 3).

12-
10
8
6
4-
2+
-12-10-22- 2
-4-
-6-
-8
-10-
8 10 12 x
What is the y-intercept of this line?

Answer 1

the y intercept is -9

Answer 2

the y-intercept of the line is -9.

Explanation:

To find the y-intercept of the line that passes through the points (1, -6) and (4, 3), we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line

First, let's calculate the slope (m) using the two given points:

Slope (m) =
`(y2-y1)/(x2-x1)`

Substituting the coordinates of the two points:

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

Now that we have the slope (m) as 3, we can use either of the given points to find the equation of the line. Let's use the point (1, -6):

y - (-6) =3(x-1)

Simplify the equation:

y + 6 = 3x - 3

Subtract 6 from both sides:

y = 3x - 9

The y-intercept is the value of y when x = 0. Substituting x = 0 into the equation:

y = 3(0) - 9 = -9

So, the y-intercept of the line is -9

i hope this helps! <3