Question

How do you graph \[3x + y = 12\] using intercepts?

Answer 1

Hint: To graph an equation using intercepts, we must find x and y intercepts. To find the x-intercept, set y = 0 and solve for x, to find the y-intercept, set x = 0 and solve for y, hence by solving we get the x and y intercepts and to graph a line, graph the points if they exist, and then connect the two points with a straight line.

Complete step-by-step answer:
Let us write the given linear equation:
  \[3x + y = 12\]
To graph the solution for the given equation, we need to find x and y intercepts.
Let us find the x-intercepts: To find the x-intercept, set y = 0 and solve for x i.e.,
 \[3x + y = 12\]
 \[3x + 0 = 12\]
 \[ \Rightarrow \] \[3x = 12\]
Divide both sides of the equation by 3 to get the value of x as
 \[\dfrac{{3x}}{3} = \dfrac{{12}}{3}\]
We get the value of x as,
 \[x = \dfrac{{12}}{3}\]
 \[ \Rightarrow \] \[x = 4\]
Hence, the x-intercept of the given equation is \[\left( {4,0} \right)\] .
Now let us find the y-intercepts: To find the y-intercept, set x = 0 and solve for y i.e.,
 \[3x + y = 12\]
 \[3\left( 0 \right) + y = 12\]
The value of y is,
 \[ \Rightarrow \] \[y = 12\]
Hence, the y-intercept of the given equation is \[\left( {0,12} \right)\] .
Now, let us graph the solution: To graph this line using the intercepts, first graph the two points as shown A = \[\left( {0,12} \right)\] and B = \[\left( {4,0} \right)\] ,then connect the two points with a straight line.

Note: The given method of finding x- and y-intercepts will be used throughout our algebraic equation, because it works for any equation. We can also use slope intercept form to graph the solution if they ask to find the slope for the given equation using the form \[y = mx + b\] and solve for x and y intercepts and any line can be graphed using two points i.e., select two x values, and plug them into the equation to find the corresponding y values.