Question

Compare the line passing through the points (−3, − 11) and (6, 4) to the line given by the equation y=32x−6.

Answer 1

See below

Explanation:

Given points:

• (-3, -11) and (6, 4)

Let's calculate it's equation:

• y = mx +b
• m = (4 + 11)/(6 +3) = 15/9 = 5/3
• y = 5/3x + b
• -11 = 5/3*(-3) + b ⇒ b = -11 + 5 = -6
• y = 5/3x - 6

The given line:

• y = 32x - 6

Compared, the lines have different slope (5/3 vs 32) but same y- intercept (-6), so both pass through the point of (0, -6). y= 32x - 6 has greater rate of change.