solve and graph 4x+3y=6
To solve and graph the equation 4x + 3y = 6, we can follow these steps:
Step 1: Solve for y
To solve for y, we need to isolate it on one side of the equation. Let's do that:
4x + 3y = 6
Subtract 4x from both sides:
3y = 6 - 4x
Next, divide both sides by 3 to solve for y:
y = (6 - 4x) / 3
So, the equation is now in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Step 2: Graph the equation
To graph the equation, we can use the slope-intercept form. From the equation y = (6 - 4x) / 3, we can identify the slope and y-intercept.
The slope (m) is the coefficient of x, which is -4/3.
The y-intercept (b) is the constant term, which is 6/3 or 2.
Start by plotting the y-intercept (0, 2) on the graph. This is the point where the line intersects the y-axis.
Next, use the slope to find another point on the line. The slope -4/3 means that for every 3 units to the right we move, we should move 4 units down.
Starting from (0, 2), move 3 units to the right. Then, move 4 units down. This gives us the point (3, -2).
Plot this point on the graph as well.
Finally, draw a straight line that passes through both points. This line represents the graph of the equation 4x + 3y = 6.
Note: If you want to have more points to plot, you can choose additional x-values and substitute them into the equation to find the corresponding y-values.
Here's an example graph for the equation 4x + 3y = 6:
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In the graph, the points (0, 2) and (3, -2) lie on the line, and the line extends infinitely in both directions.