Question

use the drawing tool to form the correct answer on the provided graph. draw a line that is parallel to line on the graph and passes through the point (-1,0).

Explanation:

Step1: Determine the slope of the given line

First, we need to find the slope of the original line. Let's take two points on the original line. From the graph, we can see that the original line passes through \((2, 0)\) and \((0, -5)\) (we can check the intercepts). The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So, \(m=\frac{0-(-5)}{2 - 0}=\frac{5}{2}\).

Step2: Use the point - slope form to find the equation of the parallel line

Since parallel lines have the same slope, the slope of the line we want to draw is also \(\frac{5}{2}\). We use the point - slope form of a line \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-1,0)\) and \(m = \frac{5}{2}\).

Substituting the values into the formula: \(y-0=\frac{5}{2}(x + 1)\), which simplifies to \(y=\frac{5}{2}x+\frac{5}{2}\).

To draw the line, we can find another point on the line. When \(x = 1\), \(y=\frac{5}{2}(1)+\frac{5}{2}=\frac{5 + 5}{2}=5\). So, the line passes through \((-1,0)\) and \((1,5)\) (and other points). We can use the "Line" tool in the drawing interface to connect the point \((-1,0)\) with another point on the line with slope \(\frac{5}{2}\) (for example, moving 2 units to the right and 5 units up from \((-1,0)\) gives the point \((1,5)\)).

Answer:

To draw the line:

1. Select the "Line" tool from the drawing tools.
2. Plot the point \((-1,0)\) (it is already marked on the graph).
3. Find another point on the line with slope \(\frac{5}{2}\) from \((-1,0)\). For example, starting at \((-1,0)\), move 2 units to the right (increase \(x\) by 2) and 5 units up (increase \(y\) by 5) to get the point \((1,5)\).
4. Use the "Line" tool to draw a line connecting \((-1,0)\) and \((1,5)\) (or any other two points on the line with slope \(\frac{5}{2}\) passing through \((-1,0)\)).