Final answer:
The slope-intercept equation for a line that passes through (-3,2) and (4,-19) is y = -3x - 7.
Step-by-step explanation:
The slope-intercept equation for a line is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula m = (y2 - y1) / (x2 - x1). Given the points (-3,2) and (4,-19), the slope can be calculated as follows: m = (-19 - 2) / (4 - (-3)) = -21 / 7 = -3. Substituting the slope and one of the points into the equation, we get: y = -3x + b. Using (-3,2), we can find the value of b: 2 = -3(-3) + b. Solving for b, we get: b = 2 - 9 = -7. Therefore, the slope-intercept equation for the line is y = -3x - 7.