Question

How do you graph the line $ x + 3y = 3 $ ?

Answer 1

Hint: We will use intercept form to determine the points of the given equation. And, we will also solve this question by assuming the value of $ x = 0 $ , by applying the value of $ x $ , we will get the coordinate of $ y $ . Then, we will assume the value of $ y = 0 $ , by which we will get the $ x $ coordinate. Finally, we will plot the points in the graph.

Complete step-by-step answer:
Here, we will graph $ x + 3y = 3 $ .
Now, we will write the equation in the slope- intercept form i.e., $ y = mx + b $ $ \to \left( 1 \right) $
Where the $ m $ is the slope
 $ b $ is the $ y $ - intercept
Then, we have $ 3y = 3 - x $
 $ y = \dfrac{{3 - x}}{3} $
 $ y = \dfrac{3}{3} - \dfrac{x}{3} $
 $ y = - \dfrac{1}{3}x + 1 $ $ \to \left( 2 \right) $
By comparing equation $ \left( 1 \right) $ and $ \left( 2 \right) $ , we have
 $ m = - \dfrac{1}{3} $ i.e., the slope of the equation
 $ b = 1 $ i.e., the $ y $ - intercept
The $ y $ - intercept is the point where the line intersects the $ y $ -axis.
Therefore, the point is $ \left( {0,1} \right) $ .
Slope is the ‘steepness’ of the line, also commonly known as rise over run i.e., $ \dfrac{{rise}}{{run}} $ . Here, $ m = - \dfrac{1}{3} $ therefore, we can say that the graph “rise” $ - 1 $ point upwards and “run” $ 3 $ points to the right from the $ y $ - intercept.
Now, we know the slope and the $ y $ - intercept, thus we also know that $ \left( {0 + 3,1 + \left( { - 1} \right)} \right) = \left( {3,0} \right) $ which will also be on the line.
Now, we know two points of the equation i.e., $ \left( {0,1} \right) $ and $ \left( {3,0} \right) $ .
Let us plot these points graphically,

Alternate method:
Now, the given equation is $ x + 3y = 3 $ .
Let us consider $ x = 0 $ , by substituting we have,
 $ 0 + 3y = 3 $
 $ 3y = 3 $
 $ y = \dfrac{3}{3} $
 $ y = 1 $
Therefore, the point is $ \left( {0,1} \right) $ .
Now, let us consider $ y = 0 $ , by substituting we have,
 $ x + 3\left( 0 \right) = 3 $
 $ x + 0 = 3 $
 $ x = 3 $
Therefore, the point is $ \left( {3,0} \right) $
Hence, the points are $ \left( {0,1} \right) $ and $ \left( {3,0} \right) $ .
Now, let us plot the points graphically,

Note: Equation of straight line is usually written in the slope-intercept form. When we are given an equation in slope- intercept form, we can use the $ y $ - intercept as the point, then out the slope from there. When an equation of a line is not given in slope-intercept form, our first step will be to solve the equation for $ y $ . Sometimes the slope intercept form will be called as $ y $ -form.