Answer:
a) Infinite solutions = intersect at every point (2 of the same line)
m = rise/run = 3/2
b = y-intercept = (0, -3)
y = 3/2x - 3
b) No solutions = no point of intersection (parallel lines)
m = 3/2 (same slope b/c parallel)
b = (0, 2)
y = 3/2x + 2
c) One solution = one point of intersection
Solution = (4, 3)
y - y₁ = m (x - x₁)
y - 2 = m (x - 2)
m = [tex]\frac{y2-y1}{x2-x1}=\frac{3-2}{4-2} =\frac{1}{2}[/tex]
y - 2 = 1/2 (x - 2)
y = 1/2x + 1
Check to see if (4, 3) is the solution to the system:
y = 1/2x + 1
y = 3/2x - 3
1/2x + 1 = 3/2x - 3
1 = 2/2x - 3
x = 4 ✅
y = 1/2(4) + 1 = 3 ✅
I hope this helps!
