Question

How do you graph x + 2y = 10 by plotting points?

Answer 1

Hint: In this problem, the given equation has to be solved which is in the form of a linear equation in one variable. You should know the general form of the equation of a straight line i.e. y = mx + c which is to be used. Equation will be converted in the form of y = mx + c. The obtained value will be finally plotted on the graph.

Complete step by step solution:
Now, let’s discuss the question now.
We all know that the slope-intercept form is a general form of a straight line and can be expressed as y = mx + c where ‘m’ is a slope and c is a constant and intercepts are m and c. So, if we wish to plot a straight line, first we have to convert the given equation in a slope-intercept form.
Now, write the equation given in question.
$\Rightarrow $x + 2y = 10
Leave y alone and take all the terms on the other side:
$\Rightarrow $2y = -x + 10
Divide the equation by 2:
$y=\dfrac{-1}{2}x+5$
Now, we obtained the equation in the form of y = mx + c where m = $\dfrac{-1}{2}$ and c = 5.
Now, we will find the intercepts for x and y.
Let’s find y-intercept first. Substitute x = 0 in equation(i) we get:
$\Rightarrow $y = $\dfrac{-1}{2}(0)+5$
Now we get the value of ‘y’ as:
$\Rightarrow $y = 5
$\therefore $y-intercept form is: $\left( 0,5 \right)$
Similarly, we will find x-intercept now. Put y = 0 in equation(i) we get:
$\Rightarrow $(0) = $\dfrac{-1}{2}x+5$
Take 5 on the other side:
$\Rightarrow $0-5 = $\dfrac{-1}{2}x$
$\Rightarrow -5=\dfrac{-1}{2}x$
Now, take $\dfrac{-1}{2}$ on the other side and solve for ‘x’:
$\Rightarrow -5\times \dfrac{2}{-1}=x$
Value of ‘x’ is:
$\therefore x=10$
$\therefore $x-intercept form is: $\left( 10,0 \right)$
Finally we will plot the graph of the equation with the help of the intercepts.

(0, 5) is y-intercept and (10, 0) is x-intercept.

Note: Points are plotted by slope and intercept form so that it becomes easy so solve for a particular variable. That’s why it is the easiest approach of finding the intercepts. You need to know the general form of the equation of the straight line and if you are not obtaining a straight line after plotting the points, it means you are going wrong somewhere in the calculation.