Final answer:
To find the slope-intercept form of the equation given two points, calculate the slope using the change in y and x, and find the y-intercept by substituting one of the points in the equation y = mx + b. Finally, write the equation in slope-intercept form.
Step-by-step explanation:
To find the slope-intercept form of the equation given two points, we need to find the slope and the y-intercept. The slope, denoted by m, is calculated as the change in y divided by the change in x between the two points. In this case, the change in y is -3 - (-1) = -2, and the change in x is 4 - 3 = 1. So the slope is -2/1, which simplifies to -2.
To find the y-intercept, we can substitute one of the given points into the slope-intercept form y = mx + b and solve for b. Let's use the point (3, -1): -1 = -2(3) + b. Solving this equation, we get b = 5.
Therefore, the slope-intercept form of the equation is y = -2x + 5.
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