Chapter 8.7, Problem 38HP

To determine

To find the quadrants through which the graph of the line pass

Answer to Problem 38HP

The graph of line with a negative slope and a positive y-intercept passes through the quadrants 1, 2 and 4

Explanation of Solution

Given information: The graph of line has a negative slope and a positive y-intercept

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Let us assume an equation of line such that the line has a negative slope and a positive y-intercept be

  $y=-2x+2$

Plot the graph of the above equation:

When $x=0$

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

When $y=0$

  $\begin{array}{l}0=-2x+2\\ 2x=2\\ x=1\end{array}$

Graph of the equation by plotting the points $\left(0,2\right)$ and $\left(1,0\right)$

  

From graph, the line passes through quadrants − 1, 2 and 4

Conclusion:

Hence, the graph of line with a negative slope and a positive y-intercept passes through the quadrants 1, 2 and 4