Question

1. the figure shown is not drawn to scale and z = y + 20 a. what is the value of x? b. what is the value of y? c. what is the value of z? 4. what is the equation of the line shown? y = \frac{4}{1}x - 5

Explanation:

Step1: Analyze angle - relationships

From the figure, we assume that \(x\) and the \(55^{\circ}\) angle are supplementary (since they form a straight - line pair). So \(x = 180 - 55=125^{\circ}\).

Step2: Use the given equation \(z=y + 20\)

We know that \(y\) and the \(55^{\circ}\) angle are vertical angles. Vertical angles are equal, so \(y = 55^{\circ}\).

Step3: Calculate \(z\)

Substitute \(y = 55^{\circ}\) into the equation \(z=y + 20\). Then \(z=55 + 20=75^{\circ}\).

Step4: Find the equation of the line

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
The line passes through the points \((0,-5)\) (so \(b=-5\)) and \((1,-1)\). The slope \(m=\frac{-1-(-5)}{1 - 0}=\frac{-1 + 5}{1}=4\). So the equation of the line is \(y = 4x-5\).

Answer:

a. \(x = 125\)
b. \(y = 55\)
c. \(z = 75\)

1. \(y = 4x-5\)