Final answer:
To find the equation of the line passing through two points, (-2,4) and (6,0), we can use the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of the line that passes through the points (-2,4) and (6,0), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1,y1) are the coordinates of one point and m is the slope of the line.
First, let's find the slope using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the given coordinates, we get m = (0 - 4) / (6 - (-2)) = -4/8 = -1/2.
Now, we can choose one of the points, say (-2,4), and plug it into the point-slope form along with the slope: y - 4 = (-1/2)(x - (-2)). Simplifying this equation will give us the final result.
To find the equation of the line that passes through the points (-2, 4) and (6, 0), we first need to calculate the slope (m) using the slope formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates, we get m = (0 - 4) / (6 - (-2)) = -4 / 8 = -1/2. With the slope and a point, (-2, 4), we can use the point-slope form of a line, y - y1 = m(x - x1), which yields y - 4 = (-1/2)(x + 2). Simplifying this leads us to the equation of the line: y = -1/2x + 3.