Final answer:
The equation for a line passing through the points (6,0) and (-12,15) is y = (-5/6)x + 5.
Step-by-step explanation:
The equation for a line that passes through the points (6,0) and (-12,15) can be found using the formula for the slope-intercept form of a line, which is y = mx + b. Here, m represents the slope and b represents the y-intercept.
First, we can calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (15 - 0) / (-12 - 6) = 15 / -18 = -5/6.
Next, we can use one of the points along with the slope to find the value of b. Let's use the point (6,0). Substituting the values into the formula, we get 0 = (-5/6)(6) + b. Simplifying, we find that b = 5.
Therefore, the equation for the line passing through the points (6,0) and (-12,15) is y = (-5/6)x + 5.