Question

X values = -6, 2 and 10. y values = 1, 3 and 5. Which equation is satisfied by all the points in the table?

dont really know how to solve this and am struggling to get a better grasp of it

Answer 1

`y=1/4x+5/2`

Explanation:

.

`x=-6, 2, 10` and `y=1,3,5`

This means the coordinates of these three points are:

`(-6,1)`, `(2,3)`, and `(10,5)`

Let's first see if they can be on a straight line. If a straight line goes through the first two points its slope would be:

`m=(y_2-y_1)/(x_2-x_1)=(3-1)/(2-(-6))=2/(2+6)=2/8=1/4`

If a straight line goes through the second and third point its slope would be:

`m=(5-3)/(10-2)=2/8=1/4`

This means all three points are on one straight line with a slope of `1/4`. Therefore, the equation of the line can be written in the form of `y=mx+b`:

`y=1/4x+b`

`b` is the `y`-intercept of the line and we can solve for it by using the coordinates of either one of the three points. We will use the first point:

`1=1/4(-6)+b`

`1=-3/2+b`

`b=1+3/2=5/2`

Then the equation of the line is:

`y=1/4x+5/2`