graph
x + 4y = 12
We can't draw graphs on this forum. Sorry.
however, since the equation is that of a straight line, just pick two points that satisfy the equation, and draw a line between them.
Which two? Doesn't matter, but the easiest ones to calculate are when x=0 or y=0.
So, since (0,3) and (12,0) lie on the line, plot them and draw the line.
To graph the equation x + 4y = 12, we can start by rearranging the equation to solve for y:
x + 4y = 12
Subtract x from both sides:
4y = 12 - x
Divide both sides by 4:
y = (12 - x) / 4
Now that we have the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we can identify the slope and y-intercept.
The slope is the coefficient of x, which is -1. The y-intercept is the constant term, which is 3.
So, the equation in slope-intercept form is y = -1/4x + 3.
To graph the equation, plot the y-intercept point at (0, 3), which is the point where the graph intersects the y-axis. Then, use the slope (-1/4) to find one or two more points and connect them to draw the line.
To find additional points, you can choose any x-values and substitute them into the equation to solve for y. For simplicity, let's choose x = 4 and x = 8:
For x = 4:
y = -1/4 * 4 + 3
y = -1 + 3
y = 2
So, another point on the graph is (4, 2).
For x = 8:
y = -1/4 * 8 + 3
y = -2 + 3
y = 1
Another point on the graph is (8, 1).
Now we have three points: (0, 3), (4, 2), and (8, 1). Plot these points on a coordinate plane and connect them to draw a straight line. This line represents the graph of the equation x + 4y = 12.