Question

Find the line equation for a line that passes through (a, b) and (2a, 3b). Suppose 'a' does not equal 0.

a) y = (2b/a)x - b
b) y = (3/2)x - (b/2)
c) y = (3b - b)/(2a)x
d) y = (3b - b)/(2a)x + b

Answer 1

The correct line equation for a line that passes through points (a, b) and (2a, 3b) is y = (2b/a)x - b, which is found by calculating the slope and applying the point-slope form.

Step-by-step explanation:

To find the equation of the line that passes through the points (a, b) and (2a, 3b) when 'a' does not equal 0, we first need to calculate the slope ('m') of the line. Recall that the slope formula is m = (y2 - y1) / (x2 - x1), which in this case becomes m = (3b - b) / (2a - a). Simplifying, we get m = 2b / a.

Next, we use the point-slope form of the line equation, which is y - y1 = m(x - x1). Plugging in one of the points (a, b) and the slope we found, we have y - b = (2b/a)(x - a). Now we distribute the slope on the right side of the equation to get y - b = (2b/a)x - 2b and then add b to both sides of the equation to solve for y. The final equation is y = (2b/a)x - b.

This matches option a from the provided choices. Thus, the correct equation for the line is y = (2b/a)x - b.