Final answer:
To find the equation of the line in slope-intercept form that passes through the points (3,-9) and (0, -1), calculate the slope and then use the y-intercept to write the equation. The final equation of the line is y = (-8/3)x - 1.
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope (m) of the line that passes through the points (3,-9) and (0, -1), we use the formula m = (y2 - y1) / (x2 - x1). Therefore, the slope m = (-1 - (-9))/(0 - 3) = 8 / -3.
Now, we know that the line passes through the point (0, -1), which is also the y-intercept of the line. Hence, the equation of the line is y = mx + b, which becomes y = (-8/3)x - 1. This is the equation of the line in slope-intercept form.