# In the coordinate system above, which of the following…

## Solution:

We start by defining the equation of line l using the slope-intercept form of a line (y = mx + b), where m = slope and b = the y-intercept.

Notice that line l has two points: (0,2) and (3,0). We can use these two points to determine the slope. The formula for slope is:

m = (change in y)/(change in x) or

m = (y_2 – y_1)/(x_2 – x_1)

Plugging in our points we have:

m = (0 – 2)/(3 – 0)

m = -2/3

We also see from the diagram that the y-intercept of line l is 2. Substituting the slope and the y-intercept into the line equation we have:

y = (-2/3)x + 2

The final step is to recognize that the answer choices are in a different form than is our equation for line l. Thus, we have to manipulate our equation such that it will match one of the answer choices. Let’s first multiply the entire equation by 3. This gives us:

3y = -2x + 6

Then add 2x to both sides of the equation:

2x + 3y = 6

**Answer: B**