Question

x|y
0=-8
1=-7 1/2
2=-7
3=-6 1/2
Which equation describes the function shown in the mapping diagram?

Answer 1

To derive a linear equation from the given mapping data, we can first convert the points from the mapping into ordered pairs:

- (0, -8)
- (1, -7.5)
- (2, -7)
- (3, -6.5)

Next, we need to determine the slope (m) of the line that fits these points. The slope can be calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the first two points (0, -8) and (1, -7.5):

\[
m = \frac{-7.5 - (-8)}{1 - 0} = \frac{0.5}{1} = 0.5
\]

Now, we can use the slope-intercept form of the equation of a line, which is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. We already found that \(m = 0.5\). To find \(b\), we can substitute one of the points into the equation. Using the point (0, -8):

\[
-8 = 0.5(0) + b \implies b = -8
\]

Now we can write the equation of the line:

\[
y = 0.5x - 8
\]

So, the equation that describes the function shown in the mapping diagram is:

\[
y = 0.5x - 8
\]