Chapter 1.1, Problem 1E

Matching In Exercises 3-6, match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$y=-\frac{3}{2}x+3$

$y=\sqrt{9-x^2}$

$y=3-x^2$

$y=x^3-x$

To determine

The correct match for the equation $y=-\frac{3}{2}x+3$ with its graph.

Answer to Problem 1E

Solution: The equation $y=-\frac{3}{2}x+3$ corresponds with graph (b).The given equation is linear.

Explanation of Solution

Given: $y=-\frac{3}{2}x+3$

Linear equation of the form $y=mx+b$ with slope m and intercept b has a graph of straight line.Take twopoints from the graph (0, 3), (2, 0).

Instead of finding rate of change, first we will write the general formula:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Inserting both points to the two-point form yields the following:

$\begin{array}{l}y-3=\frac{0-3}{2-0}\left(x-0\right)\\ y=-\frac{3}{2}x+3\end{array}$

Only one graph from the given option is a straight line. In order to verify that graph (b) matches the given equation, two distinct points from the graph must be applied to the two-point form.