Final answer:
To find the equation of a line that passes through two given points, use the slope-intercept form of a line. Calculate the slope using the formula m = (y2 - y1) / (x2 - x1), substitute the slope and one set of coordinates, and solve for the y-intercept. The equation of the line in this case is y = 0.5x + 5.
Step-by-step explanation:
To find the equation of a line that passes through two given points, you can use the slope-intercept form of a line which is y = mx + b. First, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Then, substitute the slope and one set of coordinates into the equation to solve for b. Finally, write the equation of the line with the slope and y-intercept.
In this case, the two points are (-6,2) and (0,5). The slope (m) is (5 - 2) / (0 - (-6)) = 3 / 6 = 0.5. Substituting one point into the equation, we get 2 = 0.5(-6) + b. Solving for b, we find b = 5. Therefore, the equation of the line is y = 0.5x + 5.