Q. 20 - Precalculus Enhanced with Graphing Utilities

Question

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.

$5x+2y=10$.

Step-by-Step Solution

Answer

The intercepts are :

x-intercept is $\left(2,0\right)$ and y-intercept is $\left(0,5\right)$.

Step 1: Given information:

Consider the equation,

$5x+2y=10$.

Step 2: To find the x-intercept:

Let $y=0$ in the equation,

Then, $5x+2\times 0=10$

$5x=10$

$\frac{5x}{5}=\frac{10}{5}$

$x=2$

$x-intercept is (2,0).$

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then, $5\times 0+2y=10$

$2y=10$

$\frac{2y}{2}=\frac{10}{2}$

$y=5$

$y-intercept is \left(0,5\right)$.

Step 4: To draw the graph:

We can draw the graph of the equation $5x+2y=10$ by plotting the above intercepts and the points in the table below,

$x$	$y=\frac{10-5x}{2}$	$\left(x,y\right)$
$-2$	$10$	$\left(-2,10\right)$
$-1$	$\frac{15}{2}$	$\left(-1,\frac{15}{2}\right)$
$1$	$\frac{5}{2}$	$\left(1,\frac{5}{2}\right)$
$3$	$\frac{-5}{2}$	$\left(3,\frac{-5}{2}\right)$