Question

A table of values of a linear function is shown below.

Find the slope and y-intercept of the function's graph, and find the equation for the function.

Answer 1

Given:

A table of values of a linear function.

To find:

The slope, y-intercept and equation of the function.

Solution:

Take any two points on the table.

Let the points are (-1, -3) and (0, -6).

Slope of the line:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-6-(-3)}{0-(-1)}$

$m=\frac{-6+3}{0+1}$

$m=\frac{-3}{1}$

m = -3

Slope of the function = -3

y-intercept of the function is the point where x = 0.

In the table y = -6 when x = 0

y-intercept = -6

Equation of a line:

y = mx + c

where m is the slope and c is the y-intercept

y = -3x + (-6)

y = -3x - 6

Equation of a function is y = -3x - 6.