# How do you graph using the intercepts for x+2y=5?

May 30, 2018

See below

#### Explanation:

To find the intercepts, substitute in $x = 0$ to find the y-intercept and $y = 0$ to find the x-intercept, so:

Substitute $x = 0$ into $x + 2 y = 5$
$0 + 2 y = 5$
$2 y = 5$
$y = \frac{5}{2}$
Therefore, the y-intercept is $y = \frac{5}{2}$, also written as $y = 2.5$

Substitute $y = 0$ into $x + 2 y = 5$
$x + 2 \left(0\right) = 5$
$x = 5$
Therefore, the x-intercept is $x = 5$

If you do not already know so, the x-intercept is where the line touches or crosses through the x-axis and the y-intercept is where the line touches or crosses through the y-axis.

Now that you know the intercepts, simply indicate on the graph the points $\left(5 , 0\right)$(the x-intercept) and $\left(0 , 2.5\right)$ (the y-intercept) and draw a line connecting the dots, so the graph would be:

graph{x+2y=5 [-7.54, 12.46, -3.48, 6.52]}

May 30, 2018

$x + 2 y = 5$
graph{(x^2+(y-5/2)^2-0.01)((x-5)^2+y^2-0.01)(x+2y-5)=0 [-2.59, 7.273, -0.85, 4.08]}

#### Explanation:

Given the linear equation $x + 2 y = 5$

{:
(x"-intercept=value of "x" when "y=0," | ",y=0rArrx=5," | ","point: "(5,0)),
(y"-intercept=value of "y" when "x=0," | ",x=0rArry=5/2," | ","point: "(0,5/2))

Plotting each of the two points on the Cartesian plane and drawing a line through them gives the graph shown in the Answer.
:}