Chapter B, Problem 28E

To determine

To calculate: To find the slope and y-intercept of the line and then draw its graph

Answer to Problem 28E

Slope of line is $-\frac{4}{5}$ and y-intercept of line is $2$

Explanation of Solution

Given information: Equation is $4x+5y=10$

Formula Used:

Slope intercept form of line is

  $y=mx+c$

Where,

  $m=$ Slope

  $c=$ y-intercept

Calculation:

Equation of line is given as follows:

  $4x+5y=10$

Rewriting the equation as follows:

  $\begin{array}{l}5y=-4x+10\\ y=-\frac{4}{5}x+\frac{10}{5}\\ y=-\frac{4}{5}x+2\end{array}$

Comparing the above equation with slope-intercept form of line $y=mx+c$ ,

  $\begin{array}{l}m=-\frac{4}{5}\\ c=2\end{array}$

Finding the points that lie on equation:

When $x=0$

  $\begin{array}{l}y=-\frac{4}{5}\left(0\right)+2\\ y=2\end{array}$

When $x=5$

  $\begin{array}{l}y=-\frac{4}{5}\left(5\right)+2\\ y=-4+2\\ y=-2\end{array}$

When $x=10$

  $\begin{array}{l}y=-\frac{4}{5}\left(10\right)+2\\ y=-8+2\\ y=-6\end{array}$

Thus, $\left(0,2\right),\left(5,-2\right),\left(10,-6\right)$ are the solution of equation and must lie on the equation.

Plotting the points on graph,

  y-axis

    x-axis

Conclusion:

Hence, slope of line $-\frac{4}{5}$ and y-intercept of line is $2$