To write a linear equation of the form \( y = mx + b \) based on the provided table, we first need to identify the slope (m) and the y-intercept (b) from the data given.
Here's the data you provided in tabular form:
\[ \begin{align*} x & : 0, 5, -10, 10 \ y & : 8, 5, -28, -28 \ \end{align*} \]
The coordinates can be summarized as:
- (0, 8)
- (5, 5)
- (-10, -28)
- (10, -28)
Step 1: Calculate the slope (m)
We can use two points to calculate the slope \(m\). Let's use the points (5, 5) and (0, 8).
The formula for slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using points (5, 5) and (0, 8): \[ m = \frac{5 - 8}{5 - 0} = \frac{-3}{5} = -\frac{3}{5} \]
Step 2: Find the y-intercept (b)
The y-intercept \(b\) can be found using one of the points. Since we know the point (0, 8) corresponds to \(x = 0\), we can directly use it: \[ b = 8 \]
Conclusion
Now that we have the slope \(m = -\frac{3}{5}\) and the y-intercept \(b = 8\), we can write the equation of the line in slope-intercept form:
\[ y = -\frac{3}{5}x + 8 \]
Thus, the final equation is: \[ y = -\frac{3}{5}x + 8 \]
1 answer