If the linear equation 5x - 2y = 10 is graphed, what is the y-intercept?

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Question: If the linear equation 5x - 2y = 10 is graphed, what is the y-intercept?

Options:

Correct Answer: 2

Solution:

Setting x = 0 in the equation gives y = -5, so the y-intercept is -5.

If the linear equation 5x - 2y = 10 is graphed, what is the y-intercept?

If the linear equation 5x - 2y = 10 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 when a line crosses the y-axis, the value of x is always 0.
Step 3: Substitute x = 0 into the equation 5x - 2y = 10.
Step 4: Replace x in the equation: 5(0) - 2y = 10.
Step 5: Simplify the equation: 0 - 2y = 10.
Step 6: This simplifies to -2y = 10.
Step 7: To find y, divide both sides by -2: y = 10 / -2.
Step 8: Calculate the result: y = -5.
Step 9: Therefore, the y-intercept is -5.

Linear Equations – Understanding how to manipulate and interpret linear equations in the form of y = mx + b.
Finding the y-intercept – Knowing that the y-intercept occurs where x = 0 and how to substitute this value into the equation.