Question

equation of line a:
x + 3y = 3
select values from line b:
x | y
-3 | -4
-2 | 0
-1 | 4
0 | 8
answer attempt 1 out of 2
the slope of line a is and the slope of line b is . therefore the slope of
line a is the slope of line b.

Explanation:

Step1: Find slope of Line A

Rewrite \(x + 3y = 3\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope).
Subtract \(x\) from both sides: \(3y=-x + 3\).
Divide by 3: \(y=-\frac{1}{3}x + 1\). So slope of Line A (\(m_A\)) is \(-\frac{1}{3}\).

Step2: Find slope of Line B

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Take two points from Line B's table, e.g., \((-3,-4)\) and \((-2,0)\).
\(m_B=\frac{0 - (-4)}{-2-(-3)}=\frac{4}{1} = 4\). (We can check with other points: \((-2,0)\) and \((-1,4)\): \(\frac{4 - 0}{-1-(-2)}=\frac{4}{1}=4\); consistent.)

Step3: Compare slopes

Compare \(-\frac{1}{3}\) and \(4\). Since \(-\frac{1}{3}<4\), the slope of Line A is less than the slope of Line B.

Answer:

The slope of Line A is \(-\frac{1}{3}\) and the slope of Line B is \(4\). Therefore the slope of Line A is less than the slope of Line B.