Final answer:
The equation of a line containing the points (4,-8) and (-5,1) is found by calculating the slope and using it with one of the points to determine the y-intercept. The result in slope-intercept form is y = -x - 4.
Step-by-step explanation:
To find the equation of a line in slope-intercept form that contains the points (4,-8) and (-5,1), we first need to calculate the slope (m). The slope formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the points on the line. So for our points, the slope m is (1 - (-8)) / (-5 - 4) = 9 / -9 = -1.
Next, we use one of the points and the slope to find the y-intercept (b) of the line. We can use the point-slope form: y - y1 = m(x - x1) and plug in m = -1 and the coordinates (4, -8): y - (-8) = -1(x - 4). Simplify to get the slope-intercept form: y = -1x + 4 - 8, which simplifies further to y = -x - 4.
Therefore, the equation of the line in slope-intercept form is y = -x - 4.