To find the equation in slope-intercept form (y = mx + b) from the provided table, we need to determine both the slope (m) and the y-intercept (b).
First, let's extract the coordinates from the table:
- (-2, -7)
- (-1, -4)
- (0, -1)
- (1, 2)
- (2, 5)
Step 1: Calculate the Slope (m)
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 the points (0, -1) and (1, 2):
\[ m = \frac{2 - (-1)}{1 - 0} = \frac{2 + 1}{1} = \frac{3}{1} = 3 \]
Step 2: Use the Slope and a Point to Find the y-Intercept (b)
Using the slope and one of the points (we can use (0, -1) because it gives us b directly):
\[ y = mx + b \] Substituting the point (0, -1) into the equation:
\[ -1 = 3(0) + b \] \[ -1 = b \]
Step 3: Write the Final Equation
Now we have the slope (m = 3) and the y-intercept (b = -1). Thus, the equation in slope-intercept form is:
\[ y = 3x - 1 \]
So the final answer is:
\[ \boxed{y = 3x - 1} \]