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:
\[ y = 0.5x - 8 \]