Question

A table representing a linear relationship is shown.

1
2
3
4
y-24.2 -32.4 -40.6 -48.8
X
Write the equation in slope-intercept form that represents the relationship shown.
A. -8.2x + 16
B -8.2x-16
C=8.2x + 16
D.8.2x-16

Answer 1

An equation in slope-intercept form that represents the relationship shown is: B. y = -8.2x - 16

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

• x and y represent the data points.
• m represent the slope.

First of all, we would determine the slope for this table by using these points (1, -24.2) and (2, -32.4);

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope (m) = (-32.4 + 24.2)/(2 - 1)

Slope (m) = -8.2

At data point (1, -24.2) and a slope of -8.2, an equation for this line can be calculated by using the point-slope form as follows:

`y - y_1 = m(x - x_1)`

y + 24.2 = -8.2(x - 1)

y = -8.2x - 24.2 + 8.2

y = -8.2x - 16