Question

How do you graph $2x + 2y = - 4$ using intercepts?

Answer 1

Hint: In order to solve this question, we first solve the given equation and find the x-coordinates and y-coordinates by finding the values of the respective intercepts. In order to find the values of the intercepts, we first place the value of $x$ as zero to find y-intercept and then $y$ as zero to find the value of the x-intercept. We express the given equation in the intercepts form and plot the coordinates in a graph.

Complete step-by-step solution:
The given equation is $2x + 2y = - 4$, we need to express this equation in the form of its intercepts, in order to do so we first need to find the individual values of $x$ which represents the coordinates on the x-axis and $y$ which represents the values on the y-axis.
X-intercept means the point at which a line cuts the x-axis, while y-intercept refers to the point at which the given line cuts the y- axis.
X-intercepts always have their y- coordinate as zero. Thus, in order to find the value of x-intercept, let us take the value of y-coordinate as zero in the given equation - $2x + 2y = - 4$
Therefore, $2x + 2 \times 0 = - 4$
$ \Rightarrow 2x = - 4$
Dividing both sides of the equation with $2$ , we get:
$x = \dfrac{{\not{{ - 4}}}}{{\not{2}}} = - 2$
Thus the value of x-intercept is $ - 2$ , while it coordinates on the x-axis are $\left( { - 2,0} \right)$
Now in order to find the value of y-intercept, let us take the value of $x$ as zero, as the point at which a line makes the y-intercept, the value of the x-coordinate becomes zero.
Thus, placing the value of $x$ as zero in the equation $2x + 2y = - 4$, we get:
$ \Rightarrow 2 \times 0 + 2y = - 4$
$ \Rightarrow 2y = - 4$
Dividing both sides of the equation with $2$ in order to isolate $y$ , we get:
$ \Rightarrow y = - 2$
The value of y-intercept is $ - 2s$ , while its coordinates on the y-axis is $\left( {0, - 2} \right)$
Now, we know that the equation is expressed in the intercepts form in the following way: $\dfrac{x}{a} + \dfrac{y}{b} = 1$ , where $a = $ x-intercept and $b = $ y-intercept.
We express the given equation in the intercepts form: $\dfrac{x}{{ - 2}} - \dfrac{y}{2} = - 4$
Now we need to plot these points on the graph to get our required line. Our given coordinates are: $\left( { - 2,0} \right)$ and $\left( {0, - 2} \right)$ , plotting these points on the x-axis and y-axis respectively, we get:

Note: Some common properties of straight lines are:
A line which passes through origin makes zero intercept on the axes.
A horizontal line has no x-intercept and a vertical line has no y-intercept
The intercepts on the x-axis and y-axis are usually denoted by $a$ and $b$ respectively.