Question

write the linear equation that gives the rule for this table. x: -42,-16,10,36 y: 44,18,-8,-34 Write your answers as an equation with y first, followed by an equal sign

Answer 1

To find the linear equation that gives the rule for this table, we need to find the slope and y-intercept of the line that passes through the given points.

The slope of the line can be found using the formula:

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

Using the first and last pairs of points, we get:

m = (y2 - y1) / (x2 - x1) = (-34 - 44) / (36 - (-42)) = -78 / 78 = -1

So the slope of the line is -1.

To find the y-intercept, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Using the point (10, -8), we get:

y - (-8) = -1(x - 10)

y + 8 = -x + 10

y = -x + 2 - 8

y = -x - 6

Therefore, the linear equation that gives the rule for this table is:

y = -x - 6