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

1 Answer
May 17, 2018

y=1/4x+5/2

Explanation:

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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