Graph the linear relation:
[tex]3 x+4 y=12[/tex]
Answer (2)
To graph the equation 3 x + 4 y = 12 , we find the x-intercept at ( 4 , 0 ) and the y-intercept at ( 0 , 3 ) . We can plot these points on the coordinate plane and draw a straight line through them. This line represents the linear relationship given by the equation.
;
Find the x-intercept by setting y = 0 and solving for x : x = 4 .
Find the y-intercept by setting x = 0 and solving for y : y = 3 .
Plot the x and y intercepts ( 4 , 0 ) and ( 0 , 3 ) on the coordinate plane.
Draw a straight line through the two points to graph the equation 3 x + 4 y = 12 .
Explanation
Understanding the Problem We are given the linear equation 3 x + 4 y = 12 and asked to graph it. To graph a linear equation, we need to find at least two points on the line. The easiest points to find are the x-intercept and the y-intercept.
Finding the x-intercept To find the x-intercept, we set y = 0 and solve for x :
3 x + 4 ( 0 ) = 12 3 x = 12 x = 3 12 x = 4 So the x-intercept is ( 4 , 0 ) .
Finding the y-intercept To find the y-intercept, we set x = 0 and solve for y :
3 ( 0 ) + 4 y = 12 4 y = 12 y = 4 12 y = 3 So the y-intercept is ( 0 , 3 ) .
Plotting the Points and Drawing the Line Now we plot the x and y intercepts on the coordinate plane and draw a straight line through the two points. The line represents the graph of the equation 3 x + 4 y = 12 .
Final Answer The graph of the linear relation 3 x + 4 y = 12 is a straight line passing through the points ( 4 , 0 ) and ( 0 , 3 ) .
Examples
Linear equations are used in many real-world applications, such as calculating the cost of items, determining the distance traveled at a constant speed, or modeling the relationship between two variables. For example, if you are buying apples at a store and each apple costs 0.50 , t h e t o t a l cos t c anb ere p rese n t e d b y t h e l in e a re q u a t i o n y = 0.50x , w h ere x i s t h e n u mb ero f a ppl es an d y$ is the total cost. Graphing this equation can help you visualize the relationship between the number of apples and the total cost.
