To find the equation in slope-intercept form (y = mx + b) from the provided points, we first need to identify the points represented by the data you gave:
From the table:
- Point 1: (−7, −6)
- Point 2: (0, 1)
- Point 3: (7, 8)
- Point 4: (14, 15)
Let's calculate the slope (m) using any two points. We'll use the first two points: (−7, −6) and (0, 1).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in our points:
- \(x_1 = -7\), \(y_1 = -6\)
- \(x_2 = 0\), \(y_2 = 1\)
Calculating the slope: \[ m = \frac{1 - (-6)}{0 - (-7)} = \frac{1 + 6}{0 + 7} = \frac{7}{7} = 1 \]
Now that we have the slope \(m = 1\), we can use one of the points to find the y-intercept (b). We'll use the point (0, 1), which is where the line intersects the y-axis.
In slope-intercept form, when \(x = 0\), \(y = b\). So from the point (0, 1): \[ b = 1 \]
Now, we can write the equation in slope-intercept form: \[ y = mx + b \] \[ y = 1x + 1 \quad \text{or simply} \quad y = x + 1 \]
Thus, the equation that fits the points from your table is: \[ y = x + 1 \]