To write an equation in slope-intercept form (y = mx + b) from the given table of values, we first need to determine the slope (m) and the y-intercept (b).
Let's analyze the data given in the table, interpreting it as pairs of (x, y) coordinates:
- From the first row: (5, -4)
- From the second row: (10, -8)
- From the third row: (15, -12)
Now, let’s find the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We'll use the first two points for this calculation:
\[ m = \frac{-8 - (-4)}{10 - 5} = \frac{-8 + 4}{10 - 5} = \frac{-4}{5} = -\frac{4}{5} \]
Next, we can use the slope and one of the points to find the y-intercept (b). Choosing the point (5, -4):
Using the slope-intercept form: \[ y = mx + b \] Substituting the values of m and the point (5, -4): \[ -4 = -\frac{4}{5}(5) + b \] Calculating: \[ -4 = -4 + b \] So: \[ b = 0 \]
Now we have the slope and the y-intercept:
- Slope (m) = -\frac{4}{5}
- Y-intercept (b) = 0
Thus, the equation in slope-intercept form is: \[ y = -\frac{4}{5}x \]