Final answer:
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope and the y-intercept. In this case, the slope is 3 and the y-intercept is -17. Therefore, the equation of the line is y = 3x - 17.
Step-by-step explanation:
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b). The slope can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Let's use the points (3, -8) and (5, -2) to calculate the slope: m = (-2 - (-8)) / (5 - 3) = 6 / 2 = 3. Now that we have the slope, we can substitute it into the slope-intercept form along with one of the given points to find the y-intercept. Let's use the point (3, -8): -8 = 3(3) + b. Solving for b gives us b = -8 - 9 = -17.
Therefore, the equation of the line that passes through (3, -8) and (5, -2) is: y = 3x - 17.
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