Question

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

Answer 1

Hint: For finding the intercepts, first put $x = 0$and then find the value of $y$. The resulting coordinates are to be noted and then plotted. Now, put $y = 0$ and then find the value of $x$. Note down the value of the coordinates and then pot. A straight- line can be plotted on any graph with a minimum requirement of two coordinates.

Complete step-by-step answer:
The given linear equation is:
$5x + 2y = - 2$
For finding the intercepts of the linear equation,
Firstly, we put,$x = 0$ and find $y$
$ \Rightarrow 5(0) + 2y = - 2$
$ \Rightarrow 2y = - 2$
Divide the whole equation with $2$
$ \Rightarrow y = - 1$
$ \Rightarrow $The $x$-intercept is $(0, - 1)$
For the $y$-intercept, we put $y = 0$and then find the value of $x$
$ \Rightarrow 5x + 2(0) = - 2$
$ \Rightarrow 5x = - 2$
Divide the whole equation with $5$
$ \Rightarrow x = \dfrac{{ - 2}}{5}$
$ \Rightarrow $The $y$-intercept is $\left( {\dfrac{{ - 2}}{5},0} \right)$
Plotting both the $x$ and $y$-intercept on the graph, we get

Join both the points to get a line segment which on extending gives our linear line equation,$5x + 2y = - 2$.

Additional information: $x$-intercept is where the given linear line equation touches the $x$-axis.
$y$-intercept is where the given linear line equation touches the $y$-axis. After getting an answer, one must always cross-check by substituting the values back in the equation to see if they are correct. Both the values should be taken for substitution to prove that they are correct

Note:
Here, one must only remember the order of writing the values in the Pythagoras theorem. The hypotenuse is on one side while the remaining two sides are on the other side. In the Pythagorean triplet here, if we remove a common factor $\;4$ from each value then we get $\left( {3,4,5} \right)$ , which is the most basic Pythagorean triplet.