Part 1 of 2 Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form. \( (-9,7),(9,1) \) What is the point-slope form of the equation of the line? \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)

To find the point-slope form of the line that passes through the points \( (-9, 7) \) and \( (9, 1) \), we first need to calculate the slope, \( m \). The slope \( m \) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{9 - (-9)} = \frac{-6}{18} = -\frac{1}{3} \] Now that we have the slope, we can use the point-slope form of the equation, which is \( y - y_1 = m(x - x_1) \). We can use either of the two points; let’s use \( (-9, 7) \): \[ y - 7 = -\frac{1}{3}(x + 9) \] This is the point-slope form of the equation. To convert it to slope-intercept form, we distribute and simplify: \[ y - 7 = -\frac{1}{3}x - 3 \implies y = -\frac{1}{3}x + 4 \] So the equation in slope-intercept form is: 1. Point-slope form: \( y - 7 = -\frac{1}{3}(x + 9) \) 2. Slope-intercept form: \( y = -\frac{1}{3}x + 4 \)