Part 1 of 2 Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \( (4,8) \) and \( (7,14) \) Type the point-slope form of the equation of the line. (Simplify your answer. Use integers or fractions for any number in the equation.)

To find the point-slope form of the line, we first need to determine the slope \( m \). The slope can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \( (4,8) \) and \( (7,14) \): \[ m = \frac{14 - 8}{7 - 4} = \frac{6}{3} = 2 \] Now that we have the slope, we can use the point-slope form equation, which is: \[ y - y_1 = m(x - x_1) \] Using point \( (4,8) \): \[ y - 8 = 2(x - 4) \] Now, to write it in slope-intercept form \( y = mx + b \), we simplify: \[ y - 8 = 2x - 8 \\ y = 2x \] So the point-slope form of the equation is \( y - 8 = 2(x - 4) \) and the slope-intercept form is \( y = 2x \).