Final answer:
First, calculate the slope of the line using the points then write the line equation in point-slope form. Next, convert it to slope-intercept form by isolating y to find y = -1/3x + 4.
Step-by-step explanation:
To find an equation of the line that passes through the points (-3, 5) and (9, 1), we first need to calculate the slope of the line, which is the change in y divided by the change in x. The formula for the slope m is (y2 - y1)/(x2 - x1).
Plugging in the values from the points, we get (1 - 5)/(9 - (-3)) = -4/12 = -1/3. Now, using one of the given points (-3, 5) and the slope -1/3, we can write the equation in point-slope form: y - y1 = m(x - x1), which becomes y - 5 = -1/3(x + 3).
To write this in slope-intercept form, we need to solve for y. Expanding and simplifying gives us y = -1/3x - 1 + 5, and combining like terms results in the final slope-intercept form, y = -1/3x + 4.