Final answer:
The slope of line A is determined using the coordinates given for line A and found to be -2.6. Since line B is parallel to line A, it will have the same slope. The point-slope form is then used with the point through which line B passes to find the equation of line B, which is y = -2.6x + 20.8. However, this equation is not matched by any of the provided answer choices.
Step-by-step explanation:
To determine the equation of line B that is parallel to line A, we first need to establish the slope of line A. The slope formula is m = (y2 - y1) / (x2 - x1). Using points (−3, 2) and (−23, 54), the slope is:
m = (54 - 2) / (−23 + 3)
m = 52 / -20
m = -26 / 10
m = -2.6
Since line B is parallel to line A, it has the same slope, m = -2.6. We can use the point-slope form which is y - y1 = m(x - x1), where (x1, y1) is the point line B passes through, which is (−8, 0). Substituting the values, we get:
y - 0 = -2.6(x - (-8))
y = -2.6x - 2.6*(-8)
y = -2.6x + 20.8
To put the equation in slope-intercept form (y = mx + b), we simplify to:
y = -2.6x + 20.8
However, none of the given options match this equation exactly due to a different slope. Hence, there might be a typo in the question or the set of answer choices provided. In a standard multiple-choice scenario, you would select the answer that most closely represents the correct equation, which is not present among the options A, B, C, and D.