Final answer:
The equation of the line with a slope of -3/7 that passes through the point (9, -1) is y = (-3/7)x + 20/7.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. To find the equation of a line with a slope of -3/7 that passes through the point (9, -1), we can plug in the values of m and the coordinates of the point into the slope-intercept form.
Using the given slope (-3/7), the equation becomes y = (-3/7)x + b. Now we can find the value of b by substituting the coordinates of the point (9, -1) into the equation.
Plugging in the values, we get -1 = (-3/7) * 9 + b. Solving for b, we have -1 = -27/7 + b, which simplifies to b = -1 + 27/7 = -7/7 + 27/7 = 20/7.
Therefore, the equation of the line is y = (-3/7)x + 20/7.