A line has a slope of \( -\frac{3}{5} \) and passes through the point \( (-11,8) \). Write its equation in slope- intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

To find the equation of a line in slope-intercept form, we use the formula: \[ y = mx + b \] where: - \( m \) is the slope of the line, - \( b \) is the y-intercept of the line. Given that the slope of the line is \( -\frac{3}{5} \) and it passes through the point \( (-11,8) \), we can substitute these values into the formula to find the equation of the line. Substitute the slope \( m = -\frac{3}{5} \) and the point \( (-11,8) \) into the formula: \[ 8 = -\frac{3}{5}(-11) + b \] Now, we can solve for \( b \) to find the y-intercept of the line. Solve the equation by following steps: - step0: Solve for \(b\): \(8=-\frac{3}{5}\left(-11\right)+b\) - step1: Multiply the numbers: \(8=\frac{33}{5}+b\) - step2: Swap the sides: \(\frac{33}{5}+b=8\) - step3: Move the constant to the right side: \(b=8-\frac{33}{5}\) - step4: Subtract the numbers: \(b=\frac{7}{5}\) The y-intercept of the line is \( b = \frac{7}{5} \) or \( b = 1.4 \). Therefore, the equation of the line in slope-intercept form is: \[ y = -\frac{3}{5}x + \frac{7}{5} \] or \[ y = -\frac{3}{5}x + 1.4 \]