Final answer:
To find the equation of the line passing through two points, we can first calculate the slope using the formula m = (y2 - y1) / (x2 - x1), and then substitute the coordinates of one point into the equation y = mx + b to solve for the y-intercept b.
Step-by-step explanation:
To write an equation for a line in slope-intercept form y = mx + b, we need to find the values of m and b. The slope m can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points on the line. The value of b can be found by substituting the coordinates of one of the points into the equation and solving for b. Let's use the points (-1, 5) and (3, -3) as example. The slope is m = (-3 - 5) / (3 - (-1)) = -8 / 4 = -2. Substituting the coordinates of the first point into the equation, we get 5 = -2(-1) + b. Solving for b, we find b = 3. Therefore, the equation for the line is y = -2x + 3.