Question

geo 2.4 homework 100% credit until september 14, 8:00 am graph a line that is parallel 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. the line will change colors when a parallel or perpendicular line is drawn accurately. click and drag to plot a parallel line.

Explanation:

Step1: Find two points on the given line

Let's take two points on the given line. For example, when \(x = 0\), assume \(y=- 7\) and when \(y = 0\), assume \(x = 7\). So two - points are \((0,-7)\) and \((7,0)\).

Step2: Calculate the slope of the given line

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,-7)\) and \((x_2,y_2)=(7,0)\), we have \(m=\frac{0-( - 7)}{7 - 0}=\frac{7}{7}=1\).

Step3: Recall the property of parallel lines

Parallel lines have the same slope. So the slope of the line parallel to the given line is also \(m = 1\).

Step4: Graph the parallel line

To graph the parallel line, you can start from a point (say \((0,0)\)) and use the slope. Since the slope \(m = 1=\frac{\Delta y}{\Delta x}\), for every increase of \(1\) in the \(x\) - direction, the \(y\) - value increases by \(1\). You can plot several points using this rule and then draw a straight line through them.

Answer:

The slope of the given line and the parallel line is \(1\). To graph the parallel line, start from a point (e.g., \((0,0)\)) and use the slope of \(1\) (rise \(1\), run \(1\)) to plot more points and draw the line.