Question

x= -2, -1,0,1,2
y= 9, 4, -1, -6, -11
I know how I did it but I need like a more explaining thank you

Answer 1

Suppose your function y is a linear function.


Linear equation in slope-intercept form:

y = m x + b

m = the slope of a linear function = rise / run = change in y / change in x

b = y − intercept = the point where the graph of a linear equation intersect the y-axis

y − intercept is y coordinate of a poit where x coordinate = 0


In this case:

m = ( y2 - y1 ) / ( x2 - x1 ) = ( 4 - 9 ) / [ - 1 - ( - 2 ) ] = - 5 / ( - 1 + 2 ) = - 5 / 1 = - 5

m = ( y3 - y2 ) / ( x3 - x2 ) = ( - 1 - 4 ) / [ 0 - ( - 1 ) ] = - 5 / ( 0 + 1 ) = - 5 / 1 = - 5

m = ( y4 - y3 ) / ( x4 - x3 ) = [ ( - 6 - ( - 1 ) ] / ( 1 - 0 ) = ( - 6 + 1 ) / 1 = - 5 / 1 = - 5

m = ( y5 - y4 ) / ( x5 - x4 ) = [ - 11 - ( - 6 ) ] / ( 2 - 1 ) = ( - 11 + 6 ) / 1 = - 5 / 1 = - 5


For x = 0 y = - 1 so:

y − intercept b = - 1

y = m x + b

y = - 5 x - 1


Proof:

x = - 2 , y = - 5 x - 1 = - 5 * ( - 2 ) - 1 = 10 - 1 = 9

x = - 1 , y = - 5 x - 1 = - 5 * ( - 1 ) - 1 = 5 - 1 = 4

x = 0 , y = - 5 x - 1 = - 5 * 0 - 1 = 0 - 1 = - 1

x = 1 , y = - 5 x - 1 = - 5 * 1 - 1 = - 5 - 1 = - 6

x = 2 , y = - 5 x - 1 = - 5 * 2 - 1 = - 10 - 1 = - 11