Question

How do you graph the line $x+4y=4$ ?

Answer 1

Hint: We are given a linear equation in two variables whose graph has to be drawn in an XY-plane. In order to plot any equation on a graph, we must find at least two points lying on it which can be further marked and joined to sketch the graph. Hence, we shall first find the points on this function and then plot them on a graph.

Complete step-by-step solution:
We shall first find the points lying on the line whose equation is given by, $x+4y=4$.
In the given equation, we will put the values of x and y equal to zero one by one to find two simple points one of which will have its x-coordinate equal to zero and the other one would have its y-coordinate equal to zero.
Putting $x=0$in the equation, we get
$\left( 0 \right)+4y=4$
$\Rightarrow 4y=4$
Now, we shall divide both sides by 4 to find y:
$\Rightarrow \dfrac{4y}{4}=\dfrac{4}{4}$
$\therefore y=1$
Therefore, we get the point as (0,1).
Putting $y=0$in the equation, we get
$x+4\left( 0 \right)=4$
$\Rightarrow x=4$
$\therefore x=4$
Therefore, we get the point as (4,0).
Hence, the points are (0,1) and (4,0).
Plotting these points, we get the graph as:

Note: The equation is given in the slope-intercept form as $y=-\dfrac{x}{4}+1$. It has a negative slope equal to $-\dfrac{1}{4}$. A negative slope would mean that as x increases by a certain amount, y decreases by that same amount instead of increasing. Thus, that line is called a downward sloping line. The bigger the negative slope of a line, the faster it would y decrease with respect to the increase in x.