Question

le and an equation describing 2 different linear functions
function a has a table (x: -8, -7, -6, -5, -4; y: -12, -9, -6, -3, 0) and function b has equation y = 3x - 12 (assuming the missing sign is minus). select all true statements.

• function a is increasing.
• function b is decreasing.
• the slope of function b is greater.
• function b has a larger x - intercept.
• function a has a smaller y - intercept.
• the slopes of the functions are the same.
• the x - intercepts of the functions are the same.

Explanation:

Step1: Analyze Function A's slope

Use two points from Function A's table, e.g., \((-8, -12)\) and \((-7, -9)\). Slope \(m_A=\frac{-9 - (-12)}{-7 - (-8)}=\frac{3}{1}=3\). Since slope is positive, Function A is increasing.

Step2: Analyze Function B's slope

Function B: \(y = 3x - 12\) (assuming the original is \(y = 3x - 12\), as the image shows a typo). Slope \(m_B = 3\). So slopes are equal.

Step3: Check increasing/decreasing

Function A: positive slope (\(3\)) → increasing. Function B: positive slope (\(3\)) → increasing, so "Function B is decreasing" is false.

Step4: Compare slopes

\(m_A = 3\), \(m_B = 3\) → slopes are same, so "The slope of function B is greater" is false, "The slopes of the functions are the same" is true.

Step5: Find x - intercepts

Function A: Let \(y = 0\). From table, when \(x=-4\), \(y = 0\) → x - intercept \(-4\). Function B: Let \(y = 0\), \(0 = 3x - 12\) → \(x = 4\). So Function B's x - intercept (\(4\)) is larger than A's (\(-4\)), so "Function B has a larger X - intercept" is true, "The X - intercepts of the functions are the same" is false.

Step6: Find y - intercepts

Function A: Use slope - intercept form \(y = mx + b\). Using \((-4, 0)\), \(0 = 3(-4)+b\) → \(b = 12\). Function B: \(y = 3x - 12\) → \(b=-12\). So Function A's y - intercept (\(12\)) is larger than B's (\(-12\)), so "Function A has a smaller y - intercept" is false.

Answer:

• Function A is increasing.
• The slopes of the functions are the same.
• Function B has a larger X - intercept.