The equation in the tables are
line q: 3x - y = 6
line r: 4x + 9y = 4
How to write the equation
The equation graphed is written in the slope intercept form s below
y = mx + b
where
m = slope
x = intercept
Line q
the slope, m is calculated using the points on the table (2, 0) and (-3, 15)
m = (y₀ - y₁) / (x₀ - x₁)
m = (0 - 15) / (2 - (-3))
m = (-15) / (5)
m = -3
Using point (2, 0) and the point - slope formula we solve for b
y - 0 = m (x - 2), m = 3
y = 3 x - 6
-3x + y = -6
3x - y = 6
Line r
the slope, m is calculated using the points on the table (-8, 4) and (1, 0)
m = (y₀ - y₁) / (x₀ - x₁)
m = (4 - 0) / (-8 - 1)
m = (4) / (-9)
m = -4/9
Using point (1, 0) and the point - slope formula we solve for b
y - 0 = m (x - 1), m = -4/9
y =-4/9 x + 4/9
9y = -4x + 4
4x + 9y = 4