Final answer:
The equation of the line passing through the points (-6,0) and (8,7) is determined by first finding the slope, which is 0.5, and then using the point-slope form to get the final equation y = 0.5x + 3.
Step-by-step explanation:
To find the equation of the line that passes through the points (-6,0) and (8,7), we first need to determine the slope of the line. The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1). In this case, it would be m = (7 - 0) / (8 - (-6)) = 7 / 14 = 0.5.
Now that we have the slope, we can use point-slope form to find the equation of the line. The point-slope form is y - y1 = m(x - x1). Choosing one of the points, say (-6,0), we substitute into the equation to get y - 0 = 0.5(x - (-6)). Simplifying, we get y = 0.5x + 3 as the final equation of the line.
Hence, the equation of the line passing through the points (-6,0) and (8,7) is y = 0.5x + 3.