To find the equation of a line in the form \( y = mx + b \) with a given slope \( m \) and a point on the line, we can use the point-slope form of the equation first and then convert it to slope-intercept form.
We know:
- Slope \( m = 7 \)
- Point \( (1, 8) \)
Using the point-slope form: \[ y - y_1 = m(x - x_1) \] Substituting the values: \[ y - 8 = 7(x - 1) \]
Now, distribute the slope: \[ y - 8 = 7x - 7 \]
Next, add 8 to both sides to solve for \( y \): \[ y = 7x - 7 + 8 \] \[ y = 7x + 1 \]
Now we have the equation in the form \( y = mx + b \), where \( m = 7 \) and \( b = 1 \).
Thus, the equation of the line is: \[ y = 7x + 1 \]