Question

How do you graph $5x - 3y = 15?$

Answer 1

As we know that the above given equation is a linear equation in two variables. Any equation that can be represented in the form $ax + by + c = 0$, where $a, b$ and $c$ are real numbers and $a,b$ are not equal to $0$, is called linear equation in two variables. The solutions for linear equations in two variables are pairs of values, one for $x$ and one for $y$ which makes the left and right hand side of the equation equal. We should know that the graph of a linear equation is always in the form of a straight line.

Complete step by step solution:
Here the given equation is $5x - 3y = 15$, two variables $x$ and $y$, we need solutions.
Let $x = 0$, putting the value of $x$ in equation we have,
$5*(0) - 3y = 15 \Rightarrow 0 - 3y = 15$, isolating the term $y$
we get,
$y = \dfrac{{15}}{{ - 3}}$.
Therefore $y = - 5$.
Now let $y = 0$ , again putting the value of $y$ in equation,
$5x - 3(0) = 15 \Rightarrow 5x = 15$, isolating the term $x$ we get, $x = 3$. So $x = 3$.
Putting the values of $x$and $y$in tabular form, we have

$x$	$0$	$3$
$y$	$- 5$	$0$

Now we can plot the coordinates in the graph:

Here the coordinates are $A(0, - 5)$ and $B(3,0)$ in the graph above. Similarly if we take any other value for points, it will also satisfy the equation $5x - 3y = 15$.
Hence the coordinates of the given equation in the graph are $A(0, - 5)$ and $B(3,0)$.

Note: From the above solution we can conclude that each point on the line will be the solution of the equation and each solution of equation will be some point on the line. So we plot every linear equation in two variables in a graph as a straight line in a coordinate plane as in the above equation.