Question

determining the slope of a line
felix typed a certain number of words per minute to complete his essay. the number of words he typed is modeled using a straight line on a coordinate plane.
understanding the slopes of lines
the slope of a line is determined by the steepness and direction of the line. when the graph of a line shows an increase from left to right, the slope is positive. when the line decreases from left to right, the slope is negative.
points p, q, and r form △pqr. use the triangle to complete each statement.
the length of qr is 150. the length of pr is 3.
the slope of pq is the height - to - width ratio of △pqr.
enter the slope of pq: 50
points q, s, and t form △qst. use the triangle to complete each statement.
enter the length of st:
enter the length of qt:
the slope of qs is the height - to - width ratio of △qst.
enter the slope of qs:
the slope of a straight line is the same between any two points on the line. so, the slope of the line shows that felix typed words per minute.

Explanation:

Step1: Identify coordinates for relevant points

From the graph, assume \(Q\) is at \((4, 200)\), \(S\) is at \((8, 400)\), \(T\) is at \((8, 200)\).

Step2: Calculate length of \(ST\)

The \(y\) - coordinates of \(S\) and \(T\) are \(y_S = 400\) and \(y_T=200\). The length of \(ST\) is \(|y_S - y_T|=400 - 200=200\).

Step3: Calculate length of \(QT\)

The \(x\) - coordinates of \(Q\) and \(T\) are \(x_Q = 4\) and \(x_T = 8\). The length of \(QT\) is \(|x_T - x_Q|=8 - 4 = 4\).

Step4: Calculate slope of \(QS\)

The slope formula is \(m=\frac{\text{rise}}{\text{run}}\). For the line segment \(QS\), the rise is the change in \(y\) - values (\(y_S - y_Q=400 - 200 = 200\)) and the run is the change in \(x\) - values (\(x_S - x_Q=8 - 4=4\)). So the slope \(m=\frac{400 - 200}{8 - 4}=\frac{200}{4}=50\).

Step5: Determine words per minute

Since the slope of the line representing the number of words typed over time is the rate of words per minute, and the slope of the line is 50, Felix typed 50 words per minute.

Answer:

Length of \(ST\): 200
Length of \(QT\): 4
Slope of \(QS\): 50
Words per minute: 50