Final answer:
To find the slope-intercept form for the line through (6,-1) and (3,-7), calculate the slope and use it along with one of the points to solve for the y-intercept. The resulting equation is y = 2x - 13.
Step-by-step explanation:
To write an equation in slope-intercept form of the line that passes through the points (6,-1) and (3,-7), we first need to find the slope of the line.
The slope (m) of a line through any two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).
Plugging in our points gives us m = (-7 - (-1)) / (3 - 6) = (-7 + 1) / (3 - 6) = -6 / -3 = 2.
Now that we have the slope, the slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope, so we need to find b.
Using one of the points, say (6, -1), we substitute into the equation to solve for b: -1 = 2(6) + b, which simplifies to b = -1 - 12 = -13.
Thus, the final equation is y = 2x - 13.
This example illustrates how the slope and y-intercept determine the shape and position of the line on a graph.