Final answer:
The equation of a line passing through the points (-7,4) and (-6,2) is found by first calculating the slope and then using it with one of the points to find the y-intercept, resulting in the equation y = -2x - 10. However, none of the provided choices correctly represents this equation.
Step-by-step explanation:
To determine the equation of a line passing through the points (-7,4) and (-6,2), first calculate the slope (m) of the line. The slope is defined by the change in y divided by the change in x (rise over run). Here, this is:
Slope (m) = (y2 - y1) / (x2 - x1) = (2 - 4) / (-6 + 7) = -2 / 1 = -2
Now that we have the slope, we can use one of the points to find the y-intercept (b) using the formula:
y - y1 = m(x - x1)
Substitute (-7,4) into the formula:
4 = -2(-7) + b → 4 = 14 + b → b = 4 - 14 → b = -10
Therefore, the equation of the line in slope-intercept form is y = -2x - 10. However, this option was not provided in the original question. If we only have to choose from the given options, the closest one would be y = -2x - 18, though it does not represent the correct equation given the two points supplied.