To write an equation in slope-intercept form (y = mx + b) from the given table, we first need to determine the slope (m) and the y-intercept (b) of the line represented by the points in the table.
From the table, the given points are:
- (-7, 0)
- (0, 4)
- (7, 8)
- (14, 12)
Step 1: Calculate the slope (m)
We can choose any two points to find the slope. Let's take the first two points: (-7, 0) and (0, 4).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points (-7, 0) and (0, 4):
\[ m = \frac{4 - 0}{0 - (-7)} = \frac{4}{7} \]
Step 2: Determine the y-intercept (b)
The y-intercept is the value of y when x = 0. From the second point (0, 4), we see that when \(x = 0\), \(y = 4\). So, \(b = 4\).
Step 3: Write the equation
Now we can substitute the values of m and b into the slope-intercept form:
\[ y = \frac{4}{7}x + 4 \]
This is the equation in slope-intercept form that corresponds to the given table of values.