Final answer:
To determine the equation of a line in slope-intercept form, we calculate the slope using the given points and then use the point where x is zero to find the y-intercept. In this case, the equation is y = 3x.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, you need to identify two main components: the slope (m) and the y-intercept (b). The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line, we can use the two given points F(0)=0 and F(-1)=-3. The slope (m) is the change in y divided by the change in x, which is calculated as:
m = (y2 - y1) / (x2 - x1) = (0 - (-3)) / (0 - (-1)) = 3 / 1 = 3.
Now that we have the slope, we recall that F(0)=0 gives us the y-intercept directly since it indicates where the line crosses the y-axis. The y-intercept (b) is therefore 0.
The equation of the line in slope-intercept form is then y = 3x + 0, which simplifies to y = 3x.