Final answer:
To find the equation of a line that passes through two points, use the slope-intercept form of a linear equation, y = mx + b. Find the slope using the formula m = (y2 - y1) / (x2 - x1), then substitute the coordinates of one of the points to solve for the y-intercept.
Step-by-step explanation:
To find the equation of a line that passes through the points (2,4) and (0,-2), we can use the slope-intercept form of a linear equation, y = mx + b.
First, we need to find the slope, which is given by the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the two points, we get m = (-2 - 4) / (0 - 2) = -6 / -2 = 3.
Then, we can choose any of the given points to substitute into the equation. Let's use (2,4). We have 4 = 3(2) + b. Solving for b, we get b = 4 - 6 = -2.
Therefore, the equation of the line is y = 3x - 2.