Question

How do you graph $6x + 5y = 20$ ?

Answer 1

Hint:To solve this type of question start by finding the slope and y-intercept. Next, find two ordered pairs for the given equation. After that draw x-axis and y-axis on the graph paper and mark the points. Finally, check whether all the points lie on the same line.

Complete step by step answer:Given the equation $6x + 5y = 20$ .
Let us start by solving for $y$ . That is,
Start by subtracting $6\;x$ from LHS and RHS of the equation.
$6x + 5y - 6x = 20 - 6x$
$5y = 20 - 6x$
Dividing through by $5$ , that is,
$\dfrac{{5y}}{5} = \dfrac{{20}}{5} + \dfrac{{ - 6x}}{5}$
$y = 4 - \dfrac{{6x}}{5}$
We know that the slope-intercept form is $y = mx + b$ , where $m$ is the slope, and $b$ is the y-intercept.
Next, rearrange this into the slope-intercept form. That is,
$y = - \dfrac{{6x}}{5} + 4$
So here the slope is $- \dfrac{6}{5}$ and the y-intercept is $4$ .
Next to find the $x$ and $y$ coordinates, substitute two values for $x$ in the given equation. That is, first assume that $x = 0$ . Then it can be written as,
$6 \times 0 + 5y = 20$
$5y = 20$
Dividing throughout by number $5$ , we get,
$y = 4$
Next assume $x = 2$ , then,
$6 \times 2 + 5y = 20$
$12 + 5y = 20$
Take $\;12$ to the RHS, we get,
$5y = 8$
$y = \dfrac{8}{5}$
Hence, when $x = 0$ then $y = 4$ and when $x = 2$ then $y = \dfrac{8}{5}$ .
Therefore we can graph the line using the $x$ and $y$ coordinates as shown below.

Note:
Always remember that in the case of a linear equation in two variables the graph will be a straight line. A minimum of two ordered pairs should be found for drawing the graph. If possible it is always advised to find four ordered pairs to draw the graph. Also, remember that $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept is known as the slope-intercept form. The graph can either be created using the slope and y-intercept values or using the ordered pairs obtained.