Question

area: ____ perimeter: ____

1. a) write the equation of the line on the graph shown at right. hint: y=mx+b

equation: _______________

b) solve ( 2x + 4y = -16 ) for ( y ) and graph on the same axes as part (a).

( y = )__________ (( mx + b ))

c) are the lines parallel, perpendicular, or neither? explain how you know.

1. when she was younger, mary had to look up at a ( 68^circ ) angle to see into her father’s eyes whenever she was standing 15 inches away. how high above the flat ground were her father’s eyes if mary’s eyes were 32 inches above the ground? hint: after finding how high above the ground her father’s eyes are, what should you do with the 32 inches from the ground to mary’s eyes?

Explanation:

Part 7a:

Step1: Identify slope (m)

From the graph, the line passes through \((-1, 0)\) and \((0, 4)\). Slope \(m = \frac{4 - 0}{0 - (-1)} = 4\).

Step2: Identify y-intercept (b)

The line crosses the y-axis at \((0, 4)\), so \(b = 4\).

Step3: Write equation

Using \(y = mx + b\), substitute \(m = 4\) and \(b = 4\). So equation is \(y = 4x + 4\).

Step1: Solve for y

Start with \(2x + 4y = -16\). Subtract \(2x\): \(4y = -2x - 16\). Divide by 4: \(y = -\frac{1}{2}x - 4\).

Step1: Compare slopes

Slope of part (a) line: \(m_1 = 4\). Slope of part (b) line: \(m_2 = -\frac{1}{2}\).

Step2: Check parallel/perpendicular

Parallel: slopes equal? \(4
eq -\frac{1}{2}\). Perpendicular: product of slopes \(-1\)? \(4 \times (-\frac{1}{2}) = -2
eq -1\). So neither.

Answer:

\(y = 4x + 4\)

Part 7b: