To find the equation of the line in slope-intercept form (y = mx + b) based on the provided table of x and y values, we first need to determine the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
The slope (m) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, 7) and (2, 9):
\[ m = \frac{9 - 7}{2 - 1} = \frac{2}{1} = 2 \]
Step 2: Find the y-intercept (b)
To find the y-intercept, we can use one of the points and the slope in the equation \(y = mx + b\). Let's use the point (1, 7):
\[ 7 = 2(1) + b \] \[ 7 = 2 + b \] \[ b = 7 - 2 = 5 \]
Final Equation:
Now that we have m = 2 and b = 5, we can write the equation in slope-intercept form:
\[ y = 2x + 5 \]
This is the equation of the line that represents the data in the table.