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.

Explanation:

Step1: Find slope of given line

The given line passes through points \((5,0)\) (wait, no, looking at the graph: let's identify two points on the given blue line. Let's take \((0, -5)\)? Wait, no, the x - axis and y - axis: wait, the x - axis is vertical? Wait, no, the labels: the horizontal axis is y - axis? Wait, no, the graph has a vertical axis labeled x (from - 10 to 10) and horizontal axis labeled y (from - 10 to 10). Wait, that's a bit unusual, but let's find two points on the given line. Let's see, the line passes through \((5,0)\) (x = 5, y = 0) and \((0, - 5)\)? Wait, no, when x = 5, y = 0? Wait, no, let's check the coordinates. Wait, the vertical axis is x, horizontal is y. So a point on the line: when x = 5, y = 0? Wait, no, let's take two points. Let's say when x = 0, y=-5? No, wait, the line goes through (5,0) and (0, - 5)? Wait, no, let's calculate the slope. The slope \(m\) of a line is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: (5,0) and (0, - 5)? Wait, no, if x is vertical, then the change in x is vertical. Wait, maybe I got the axes reversed. Wait, usually, horizontal is x - axis, vertical is y - axis. But in this graph, the vertical axis is labeled x, horizontal is y. So let's re - orient: let's consider the horizontal axis as y (left - right) and vertical as x (up - down). So a point on the line: when y = 0, x = 5? No, the line crosses the y - axis (horizontal) at y=-5? Wait, no, the given line: let's take two points. Let's say (x1,y1)=(5,0) and (x2,y2)=(0, - 5). Wait, no, the slope formula is \(m=\frac{x_2 - x_1}{y_2 - y_1}\) (since x is vertical). Wait, if horizontal is y, vertical is x, then the slope (rate of change of x with respect to y) is \(m=\frac{\Delta x}{\Delta y}\). Let's take two points: when y = 0, x = 5; when y=-5, x = 0. Then \(\Delta x=0 - 5=-5\), \(\Delta y=-5 - 0=-5\). So slope \(m=\frac{\Delta x}{\Delta y}=\frac{-5}{-5}=1\). Wait, no, that can't be. Wait, maybe the axes are standard, and the labels are swapped. Maybe it's a typo, and the horizontal axis is x, vertical is y. Let's assume that (maybe the labels are swapped). So horizontal axis is x, vertical is y. Then the line passes through (0, - 5) and (5,0). Then the slope \(m=\frac{0 - (-5)}{5 - 0}=\frac{5}{5}=1\). So the slope of the given line is \(m = 1\).

Step2: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope \(m\) is \(m_{perp}=-\frac{1}{m}\). Since \(m = 1\), then \(m_{perp}=-1\).

Step3: Draw the perpendicular line

A line with slope - 1 (in the standard x - y axis, but here axes are labeled differently, but the slope concept still holds). We can plot two points for the perpendicular line. For example, if we take a point, say (0,0), then using the slope - 1, another point would be (1, - 1) (if x increases by 1, y decreases by 1) or (- 1,1) (x decreases by 1, y increases by 1). We can draw a line with slope - 1.

Answer:

The slope of the given line is \(1\), and the slope of the perpendicular line is \(- 1\). To draw the perpendicular line, use the slope \(-1\) and plot points accordingly (e.g., through \((0,0)\) and \((1, - 1)\) or other points with a slope of \(-1\)).