find any intercepts then graph the linear equation
-x+3y=9
To find intercepts, set one variable = 0. Intercept means where the graph crosses the x- or y-axis.
The x-intercept is where y=0.
-x = 9
x = -9
Intercept: (-9,0)
The y-intercept is where x=0.
3y = 9
y = 3
Intercept: (0,3)
With these two points, plot the line.
To find the intercepts of the linear equation -x + 3y = 9, we can set one of the variables to zero and solve for the other variable.
1. x-intercept: Set y = 0 and solve for x.
-x + 3(0) = 9
-x = 9
x = -9
Therefore, the x-intercept is (-9, 0).
2. y-intercept: Set x = 0 and solve for y.
-0 + 3y = 9
3y = 9
y = 3
Therefore, the y-intercept is (0, 3).
Now, let's graph the linear equation -x + 3y = 9:
- Start by plotting the x-intercept (-9, 0).
- Then, plot the y-intercept (0, 3).
- Connect these two points with a straight line.
The graph of the linear equation -x + 3y = 9 will look like this:
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3 | x x
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-9 0 x-axis
To find the x-intercept, we set y = 0 in the equation and solve for x.
So, let's substitute y = 0 in the given equation:
-x + 3(0) = 9
-x = 9
To solve for x, we need to isolate it.
Multiply both sides of the equation by -1 (or divide by -1), which will reverse the sign:
x = -9
Therefore, the x-intercept is -9.
To find the y-intercept, we set x = 0 in the equation and solve for y.
Let's substitute x = 0 in the given equation:
-0 + 3y = 9
3y = 9
To solve for y, we divide both sides of the equation by 3:
y = 3
Therefore, the y-intercept is 3.
Now we can graph the linear equation using the x-intercept (-9) and the y-intercept (3).
The x-intercept is the point (-9, 0), which lies on the x-axis.
The y-intercept is the point (0, 3), which lies on the y-axis.
Plot these two points (-9, 0) and (0, 3) on a graph. Then, draw a straight line passing through these two points.
The graph of the linear equation -x + 3y = 9 is a straight line that passes through the points (-9, 0) and (0, 3).