Final answer:
The first step in finding the equation of a line in slope-intercept form for the given points is to calculate the slope. The slope (m) is found using the formula m = (y2 - y1) / (x2 - x1), leading to a slope of -2 for the given points.
Step-by-step explanation:
The first step in finding the equation of a line that passes through the points (5, -4) and (-1, 8) in slope-intercept form is to calculate the slope of the line. According to the formula for slope (m), which is the change in y divided by the change in x (m = (y2 - y1) / (x2 - x1)), we can use the given points to find the slope. So for our points (5, -4) and (-1, 8), the slope m would be calculated as m = (8 - (-4)) / (-1 - 5).
After simplifying, m = 12 / -6, which gives us a slope of -2. Now that we have the slope, the slope-intercept form of a line is indicated by y = mx + b, where m is the slope and b is the y-intercept. With the slope known, the next step is to use one of the points to solve for the y-intercept, b. Afterwards, we can write the final equation of the line in the desired form using the calculated values of m and b.