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Suppose a line has the equation y = -3x + 5. What would the equation of the line be after it is reflected about the y-axis?

a.
y = 3x + 5
c.
y = negative 1 over 3 x plus 5
b.
y = 1 over 3 x plus 5
d.
none of the above

1 Answer

1 vote

Final answer:

The equation of the line after reflection about the y-axis is y = 3x + 5, which represents a straight line with a positive slope and an unchanged y-intercept.

Step-by-step explanation:

To find the equation of the line after it is reflected about the y-axis, we need to understand how reflection affects the line's equation.

The original line equation is y = -3x + 5, which is a straight line with negative slope.

Reflecting this line about the y-axis effectively changes the sign of the x-coefficient since the x-values on the original line will now take on the opposite sign.

Hence, the new equation for the reflected line will have a positive slope and the same y-intercept, because the y-axis itself does not change position.

Therefore, the new equation will be y = 3x + 5, maintaining the y-intercept at 5 and reversing the slope from negative to positive.

Among the given options, the correct answer is a. y = 3x + 5, which exhibits a straight line with a positive slope and whose y-intercept remains unchanged at 5.

User Pete Schlette
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