Question

problem 6: part b
here is a line.
drag the points to draw a line that is parallel.
what is the slope of each line?
explain your thinking.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For parallel lines, the slopes are equal.

Step2: Select two points on Line 1

Let's assume two points on Line 1: \((x_1,y_1)\) and \((x_2,y_2)\). Count the rise (change in \(y\)) and run (change in \(x\)). Suppose the rise is \(4\) and the run is \(1\). Then \(m_1=\frac{4}{1}=4\).

Step3: Calculate the slope of Line 2

Since Line 2 is parallel to Line 1, by the property of parallel lines (parallel lines have equal slopes), \(m_2 = m_1\). Using the same slope - calculation method (because the "steepness" (rise over run) is the same for parallel lines), if we apply the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) for Line 2 with the same ratio of vertical change to horizontal change as Line 1, \(m_2 = 4\).

Answer:

Line 1: \(4\)
Line 2: \(4\)