Final answer:
To write the slope-intercept equation for a line through (5, -1) with the same y-intercept as the line x - 3y = 6, we find the y-intercept by setting x to 0, which is -2. We then use the slope given by Figure A1, which is 3. The resulting equation is y = 3x - 2.
Step-by-step explanation:
To find the slope-intercept equation of a line that contains a point (5, -1) and has the same y-intercept as the line x - 3y = 6, we first need to determine the y-intercept of the given line. We can find the y-intercept by setting x to 0 in the given equation and solving for y:
x - 3y = 6
0 - 3y = 6
-3y = 6
y = -2
The y-intercept of the line x - 3y = 6 is (0, -2). Since we know that the slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept, and the line we're looking for has the same y-intercept of -2, our equation will have the form y = mx - 2.
Next, we need to find the slope of our new line. Since the slope is the rise over the run, and according to Figure A1, the slope of the line is 3, we can use this slope for our line equation. The complete slope-intercept form of our line is y = 3x - 2.