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Math  /  Algebra

QuestionTo use your knowledge of xx- and yy-intercepts to choose the correct graph of the equation, find the intercepts of the equation: 4x+6y=124x + 6y = 12

Studdy Solution

STEP 1

1. The equation given is 4x+6y=124x + 6y = 12.
2. We need to find both the xx-intercept and yy-intercept.
3. The intercepts will help in identifying the correct graph of the equation.

STEP 2

1. Find the xx-intercept.
2. Find the yy-intercept.
3. Use the intercepts to describe the graph.

STEP 3

To find the xx-intercept, set y=0y = 0 in the equation 4x+6y=124x + 6y = 12.
4x+6(0)=12 4x + 6(0) = 12
This simplifies to:
4x=12 4x = 12

STEP 4

Solve the equation 4x=124x = 12 for xx.
x=124=3 x = \frac{12}{4} = 3
Thus, the xx-intercept is (3,0)(3, 0).

STEP 5

To find the yy-intercept, set x=0x = 0 in the equation 4x+6y=124x + 6y = 12.
4(0)+6y=12 4(0) + 6y = 12
This simplifies to:
6y=12 6y = 12

STEP 6

Solve the equation 6y=126y = 12 for yy.
y=126=2 y = \frac{12}{6} = 2
Thus, the yy-intercept is (0,2)(0, 2).

STEP 7

The intercepts are (3,0)(3, 0) and (0,2)(0, 2). These points can be used to plot the line on a graph, where the line crosses the xx-axis at 33 and the yy-axis at 22.
The intercepts of the equation are: x-intercept: (3,0) x\text{-intercept: } (3, 0) y-intercept: (0,2) y\text{-intercept: } (0, 2)

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