Chapter 1.3, Problem 74AYU

In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility.

$\frac{1}{3}x+y=2$

To determine

To find: The slope and $y\text{-intercept}$ of the equation $\frac{1}{3}x+y=2$

Answer to Problem 74AYU

Solution:

$\text{Slope }=-\frac{1}{3}$

$y\text{-intercept }=2$

Explanation of Solution

Given:

The equation $\frac{1}{3}x+y=2$

Calculation:

To obtain the slope and $y\text{-intercept}$, write the equation in slope intercept form by solving for $y$.

$y=-\frac{1}{3}x+2$

The coefficient of $x$, $-\frac{1}{3}$, is the slope and the constant, 2, is the $y\text{-intercept}$.

Graph the line with $y\text{-intercept}$ 2 and slope $-\frac{1}{3}$. Starting at the point $\left(0,2\right)$, go 3 units to the right and 1 unit down to the point $\left(3,1\right)$. Draw the line through these points.