Question

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° 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:

Step1: Identify the trigonometric relationship

We have a right triangle where the adjacent side to the \(68^\circ\) angle is \(15\) inches, and we need to find the opposite side (height above Mary's eyes), let's call it \(h\). We use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan(68^\circ)=\frac{h}{15}\).

Step2: Calculate \(h\)

Solve for \(h\): \(h = 15\times\tan(68^\circ)\). Using a calculator, \(\tan(68^\circ)\approx2.475\), so \(h\approx15\times2.475 = 37.125\) inches.

Step3: Find father's eye height

Add Mary's eye height (32 inches) to \(h\): \(37.125 + 32=69.125\) inches.

Answer:

Approximately \(69.13\) inches (or \(69.125\) inches exactly from calculation)