Question

question
graph a line that is perpendicular to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line.
click and drag to plot a perpendicular line.
the line will change colors when a parallel or perpendicular line is drawn accurately.
answer
original slope:
perpendicular slope:

Explanation:

Step1: Find two points on the original line

Looking at the graph, the line passes through \((0, -5)\) and \((5, 0)\) (we can identify these by looking at the intersections with the axes and grid points).

Step2: Calculate the slope of the original line

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -5)\) as \((x_1, y_1)\) and \((5, 0)\) as \((x_2, y_2)\), we have:
\(m=\frac{0 - (-5)}{5 - 0}=\frac{5}{5} = 1\). So the original slope is \(1\).

Step3: Find the slope of the perpendicular line

The slope of a line perpendicular to a line with slope \(m\) is the negative reciprocal, \(m_{\perp}=-\frac{1}{m}\). For \(m = 1\), the negative reciprocal is \(-1\) (since \(-\frac{1}{1}=-1\)).

Answer:

Original Slope: \(1\)
Perpendicular Slope: \(-1\)