If the linear equation 3x + 4y = 12 is graphed, what is the y-intercept?

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Question: If the linear equation 3x + 4y = 12 is graphed, what is the y-intercept?

Options:

Correct Answer: 3

Solution:

Setting x = 0 in the equation gives y = 3, so the y-intercept is 3.

If the linear equation 3x + 4y = 12 is graphed, what is the y-intercept?

If the linear equation 3x + 4y = 12 is graphed, what is the y-intercept?

Step 1: Understand that the y-intercept is the point where the line crosses the y-axis.
Step 2: Recall that on the y-axis, the value of x is always 0.
Step 3: Substitute x = 0 into the equation 3x + 4y = 12.
Step 4: The equation becomes 3(0) + 4y = 12.
Step 5: Simplify the equation to 0 + 4y = 12, which simplifies to 4y = 12.
Step 6: Solve for y by dividing both sides by 4, giving y = 12 / 4.
Step 7: Calculate 12 / 4 to find y = 3.
Step 8: Conclude that the y-intercept is 3.

Linear Equations – Understanding how to find the y-intercept of a linear equation by substituting x = 0.
Graphing – Knowledge of how linear equations are represented graphically and the significance of intercepts.