Question

Find the equation of the linear function represented by the table below in slope-intercept form.

Answer 1

y= 8x +7

Explanation:

slope-intercept form:

y= mx +c, where m is the gradient (or slope) and c is the y-intercept.

Since it is a linear function, the gradient of any 2 points would be equal.

`gradient = (y1 - y2)/(x1 - x2)`

Thus, gradient of the line

`= (39 - 23)/(4 - 2) \\ = (16)/(2) \\ = 8`

Subst. m=8 into the equation:

y= 8x +c

To find the value of c, substitute a pair of coordinates.

When x=0, y= 7,

7= 8(0) +c

c= 7

Thus, the equation of the linear function is y= 8x +7.