A line has slope -5/3. Through which two points will could this line pass?
To find the equation of the line with a slope of -5/3, we need to find two points that lie on the line.
Let's choose a random point (x1, y1).
Since the slope is the change in y over the change in x, we can say that:
-5/3 = (y - y1)/(x - x1)
Now, let's choose another point (x2, y2).
Using the same formula, we have:
-5/3 = (y - y2)/(x - x2)
Now we have two equations:
-5/3 = (y - y1)/(x - x1)
-5/3 = (y - y2)/(x - x2)
Since the line passes through both points, the equations hold true for both points.
To simplify the equations, we can multiply both sides by 3 to get rid of the denominators:
-5 = 3(y - y1)/(x - x1)
-5 = 3(y - y2)/(x - x2)
Next, let's cross-multiply to eliminate the fraction:
-5(x - x1) = 3(y - y1)
-5(x - x2) = 3(y - y2)
Expanding both equations:
-5x + 5x1 = 3y - 3y1
-5x + 5x2 = 3y - 3y2
Now, let's simplify further:
5x - 3y = 5x1 - 3y1
5x - 3y = 5x2 - 3y2
Since the line passes through both points, the left side of the equation will be the same for both equations. Therefore, the right sides must be equal as well. This means:
5x1 - 3y1 = 5x2 - 3y2
Now, we can choose any values for x1, y1, and x2, and solve for y2. For simplicity, let's choose x1 = 0 and y1 = 0:
5(0) - 3(0) = 5x2 - 3y2
0 = 5x2 - 3y2
3y2 = 5x2
y2 = (5/3)x2
Therefore, the line could pass through the two points (0,0) and any point (x2, (5/3)x2), since they satisfy the equation of the line.