Question

1. are lines g and n parallel? check answer

Explanation:

Step1: Find two points on line g

Let's take two points on line g. From the graph, line g passes through (0, 4) and (4, 0).

Step2: Calculate the slope of line g

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points (0, 4) and (4, 0), $m_g=\frac{0 - 4}{4 - 0}=\frac{-4}{4}=- 1$.

Step3: Find two points on line n

Take two points on line n. Let's say it passes through (0, - 4) and (2, - 2) (by observing the graph).

Step4: Calculate the slope of line n

Using the slope formula, for points (0, - 4) and (2, - 2), $m_n=\frac{-2-(-4)}{2 - 0}=\frac{-2 + 4}{2}=\frac{2}{2}=1$.

Step5: Compare the slopes

Parallel lines have equal slopes. Since $m_g=-1$ and $m_n = 1$, and $-1
eq1$, the slopes are not equal.

Answer:

No, lines g and n are not parallel because their slopes are not equal (slope of g is -1 and slope of n is 1).