Final answer:
To find the equation of a line passing through two given points, you can use the slope formula and point-slope form. The equation of the line passing through (6, -2) and (-2, 4) is y = -3/4x + 5/2.
Step-by-step explanation:
To find the equation of a line passing through two given points, we can follow these steps:
Use the slope formula to find the slope: The slope formula is given by m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the two points into the formula, we get m = (-2 - 4) / (6 - (-2)) = -6/8 = -3/4.
Substitute a point and slope in point-slope form: Using the point-slope form y - y1 = m(x - x1), we can choose one of the given points and substitute its coordinates into the equation, along with the slope we found. Let's choose the point (6, -2): y - (-2) = -3/4(x - 6).
Distribute the slope through the parentheses: Simplify the equation by distributing the slope: y + 2 = -3/4x + 9/2.
Solve for the y-variable: Isolate the y-variable by subtracting 2 from both sides: y = -3/4x + 9/2 - 2 = -3/4x + 5/2.
Therefore, the equation of the line passing through the points (6, -2) and (-2, 4) is y = -3/4x + 5/2.