How do you graph using the intercepts for 5x – 5y = 10?

Hint: Here in this question, we will use the general form of the equation of slope and intercept to solve this problem. The general form of this equation is y = mx + c where m is the slope and c is the constant here that tells you to shift up or down the graph by b units. This is basically slope-intercept form which we will be using in this question.

Complete step by step answer:
Now let’s solve the question.
As we know about the slope-intercept form that it is a general form of a straight line and is expressed as y = mx + c where ‘m’ is a slope and c is a constant and intercepts are m and c.
For plotting the straight line, first, we need to convert the given equation in a slope-intercept form. Let’s see how!
Write the equation from the question.
 $ \Rightarrow $ 5x - 5y = 10
Take 5 common from the left-hand side:
 $ \Rightarrow $ 5(x - y) = 10
Now take 5 to the other side:
 $ \Rightarrow $ x – y = $ \dfrac{10}{5} $
 $ \Rightarrow $ x – y = 5
Take 5 to the left side and –y to the right side of the equation. We get:
 $ \Rightarrow y=x-5.....(i) $
Therefore, we have got our equation in the slope-intercept form i.e. y = mx + c.
Here, m = 1 and c = -5 .
Now, we have to find the intercepts for x and y.
Let’s find y-intercept first. Substitute x = 0 in equation(i) we get:
 $ \Rightarrow $ y = (0) - 5
Now we get the value of ‘y’ as:
 $ \Rightarrow $ y = -5
 $ \therefore $ y-intercept form is: $ \left( 0,-5 \right) $
Similarly, find x-intercept. Put y = 0 in equation(i) we get:
 $ \Rightarrow $ (0) = x – 5
Now the value of x will be:
 $ \Rightarrow $ x = 5
 $ \therefore $ x-intercept will be: (5,0)
Now, let’s plot the graph of the equation given in the question with the help of the intercepts.


The graph above is of y-intercept: (0,-5)


The graph above is of x-intercept: (5,0)

Note:
In this question particularly, we have to use the slope-intercept form as it is asked to graph the equation by using intercepts. Else the question can be solved by substitution also. Plot the graph neatly.