Final answer:
To find the equation of a line passing through two points, we can use the slope-intercept form, y = mx + b. The slope is 1 and the y-intercept is 8, so the equation is y = x + 8.
Step-by-step explanation:
To find the equation of a line passing through two points, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, we find the slope, m, using the formula m = (y2 - y1) / (x2 - x1). In this case, the two points are (-1, 7) and (2, 10), so the slope is (10 - 7) / (2 - (-1)) = 3/3 = 1.
Next, we substitute one of the points and the slope into the slope-intercept form to find the y-intercept, b. Using the point (-1, 7), we have 7 = 1*(-1) + b. Solving for b, we get b = 8.
Therefore, the equation of the line is y = x + 8. Answer choice C, -x + y = 8, is the correct equation.