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Math  /  Algebra

QuestionFind the intercepts of the equation. x+2y=6x+2 y=6
X-intercept (Blank 1, Blank 2) y-intercept (Blank 3, Blank 4)

Studdy Solution

STEP 1

1. The equation x+2y=6 x + 2y = 6 is a linear equation in two variables.
2. The x-intercept occurs where the graph of the equation crosses the x-axis, which means y=0 y = 0 .
3. The y-intercept occurs where the graph of the equation crosses the y-axis, which means x=0 x = 0 .

STEP 2

1. Find the x-intercept by setting y=0 y = 0 and solving for x x .
2. Find the y-intercept by setting x=0 x = 0 and solving for y y .

STEP 3

To find the x-intercept, set y=0 y = 0 in the equation x+2y=6 x + 2y = 6 :
x+2(0)=6 x + 2(0) = 6

STEP 4

Simplify the equation:
x=6 x = 6
The x-intercept is at the point (6,0) (6, 0) .

STEP 5

To find the y-intercept, set x=0 x = 0 in the equation x+2y=6 x + 2y = 6 :
0+2y=6 0 + 2y = 6

STEP 6

Solve for y y :
2y=6 2y = 6
Divide both sides by 2:
y=3 y = 3
The y-intercept is at the point (0,3) (0, 3) .
The intercepts are: X-intercept (6,0) (6, 0) Y-intercept (0,3) (0, 3)

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