Final answer:
The equation of the line through the points (1, 5) and (2, 8) is y = 3x + 2.
Step-by-step explanation:
To find the equation of a line that goes through the points (1, 5) and (2, 8), we need to first calculate the slope (m) of the line. The slope is found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. In this case, (x1, y1) = (1, 5) and (x2, y2) = (2, 8), so the slope m = (8 - 5) / (2 - 1) = 3 / 1 = 3. With the slope known, we can use point-slope form or slope-intercept form to find the equation of the line. Since we want the equation in slope-intercept form, which is y = mx + b, we can use one of the points to solve for b, the y-intercept. Using point (1, 5) and m = 3, the equation is y = 3x + b. Substituting for x and y, we get 5 = 3(1) + b. Solving for b results in b = 5 - 3 = 2. Thus, the equation of the line is y = 3x + 2.