Final answer:
The equation of line L which passes through points A(-2, -1) and B(-3, -9) can be found by calculating its slope, m = 8, and its y-intercept, b = 15, resulting in the equation y = 8x + 15.
Step-by-step explanation:
The equation of a line can be defined using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. To find the slope of line L passing through points A(-2, -1) and B(-3, -9), we use the slope formula m = (y2 - y1) / (x2 - x1). The slope m is calculated as (-9 - (-1)) / (-3 - (-2)) = -8 / -1 = 8. The slope of line L is 8.
Next, we use one of the points to find b, the y-intercept. Let's use point A(-2, -1). The equation becomes -1 = 8(-2) + b which leads to b = 16 - 1 = 15. Therefore, the equation of line L is y = 8x + 15.
To visualize this, you can construct a table plugging in values for x and solving for y, or plot the points and draw a line through them, as seen in Figure A1. The y-intercept of line L would be at y = 15 when x = 0. The slope indicates that for every increase of 1 on the x-axis, y increases by 8 on the vertical axis.