250 Graphs of Linear Relations
- Imagine two points P and Q plotted on the Cartesian plane, where the independent
variable is u and the dependent variable is v. Point P is defined by (−1,−6), and Q is
defined (2, 2). What is the slope of the line connecting these two points if we go in the
direction from P to Q? - Calculate the slope of the line in Prob. 1 on the basis of going in the direction from Q
toP, showing that the slope doesn’t depend on which way we move along the line. - Derive an equation of the line described in Probs. 1 and 2 in PS form.
- Derive an equation of the line described in Probs. 1, 2, and 3 in SI form.
- Sketch a graph of the linear equation discussed in Probs. 1 through 4 using the simplest
possible method. Label the slope as m and the v-intercept as b, and indicate their values. - Suppose we see two equations where s is the independent variable and t is the
dependent variable:
t=s+ 5
and
t= 5 − s
Someone says, “When graphed, these equations will produce lines oriented at a 90°
angle with respect to each other.” How can she say this without drawing the graphs?
Under what circumstances will she be right? Under what circumstances will she be
wrong? - Our advisor, who introduced herself in Prob. 6, goes on to make the claim, “The two
lines we talked about will intersect somewhere on the t axis.” She’s right! What is the
exact point of intersection? - Graph the two lines we discussed in Probs. 6 and 7, and label the point of intersection.
- Find an equation for the line in Cartesian (x,y) coordinates that passes through the
two points (2, 8) and (0, −4). Use the results of the last challenge. Put the equation
into PS form. - Find an equation for the line in Cartesian (x,y) coordinates that passes through the two
points (−6,−10) and (6, −12). Use the results of the last challenge. Put the equation
into SI form.