Answer:
Yes, the line passes through point C (5,3)
Explanation:
To justify this conclusion, we can find the equation of the line that passes through points A(-3,-2) and B(2,1) using the slope-intercept form.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-2)) / (2 - (-3))
m = 3/5
Step 2: Use the point-slope form to find the equation of the line. We'll use point A(-3,-2) as the reference point.
y - y1 = m(x - x1)
y - (-2) = (3/5)(x - (-3))
y + 2 = (3/5)(x + 3)
Step 3: Simplify the equation by distributing the (3/5) to the terms inside the parentheses.
y + 2 = (3/5)x + 9/5
Step 4: Subtract 2 from both sides of the equation to isolate y.
y = (3/5)x + 9/5 - 2
y = (3/5)x + 9/5 - 10/5
y = (3/5)x - 1/5
Now, we can check if point C(5,3) lies on this line by substituting its coordinates into the equation.
y = (3/5)x - 1/5
3 = (3/5)(5) - 1/5
3 = 3 - 1/5
3 = 3
Since the equation holds true when we substitute the coordinates of point C(5,3), we can conclude that the line passes through point C as well.