Final answer:
The slope of the line passing through (-9, 5) and (-3, 3) is -1/3. After finding the y-intercept to be 2, the correct equation in slope-intercept form is y = -1/3x + 2, which does not match any of the given options.
Step-by-step explanation:
To find the equation of the line that passes through the points (−9, 5) and (−3, 3), we first need to calculate the slope of the line. The slope formula is (y2−y1)/(x2−x1). Plugging in our values gives us (3−5)/(−3−(−9)) = (3−5)/(−3+☓9) = −2/6 = −1/3, so the slope is −1/3.
Now, we use the slope-intercept form of a line's equation, which is y = mx + b, where m is the slope and b is the y-intercept. We already have m = −1/3, and now we need to find b. We can do this by plugging in the x and y values from one of the points and solving for b. Let's use the point (−3, 3):
3 = (−1/3)(−3) + b
3 = 1 + b
b = 3−1
b = 2
Therefore, the equation of the line in slope-intercept form is y = −1/3x + 2. However, this equation is not one of the options provided, indicating a possible error in the question or answer choices. None of the options presented is correct based on our calculation.