Final answer:
To find the equation of the line, we calculated the slope (3) using the two given points and then used one point to find the y-intercept (-10). The final equation in slope-intercept form is y = 3x - 10, which corresponds to option D.
Step-by-step explanation:
The question asks us to find the equation of a line in slope-intercept form that passes through the points (4,2) and (6,8). To solve this, we first need to determine the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points. Substituting the given points into the formula, we get:
m = (8 - 2) / (6 - 4) = 6 / 2 = 3
Next, we use the slope-intercept form of the equation, y = mx + b, where m is the slope and b is the y-intercept. Substituting the slope and one of the points into the equation to solve for b, we get:
2 = 3(4) + b
b = 2 - 12
b = -10
Thus, the equation of the line is y = 3x - 10. Among the provided options, D. y = 3x - 10 is the correct equation in slope-intercept form.