Blue Book/math / page 398 #14

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<p>page 398 #14</p>

<p>This was a simple question, but I just wanted to know the rules for reflecting lines across x and y-axis. </p>

<p>"If line l is y=2x+5, and line p is line l reflected in the x-axis, what is the equation of line p?"</p>

<p>The answer is y=-2x-5. Now I'm asking what does a reflection in the x-axis do to a line? does it negate both the slope and the y-intercept? And if so, what does a reflection in the y-axis do?</p>

<p>Another one was page 400 # 18:
I wasn't sure how III b <= f(a) was true.</p>

<p>Thanks.</p>

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<p>For the first problem, think of it this way:</p>

<p>When you reflect across the x-axis, you change point (x,y) to point (x,-y). Thus you replace (y) with (-y) in your given equation.</p>

<p>If you start off with y=mx+b, you end up with y=-mx-b, so yes, reflection across the x-axis negates both the slope and y-intercept.</p>

<p>When you reflect across the y-axis, you change point (x,y) to point (-x,y). Thus you replace (x) with (-x) in your given equation.</p>

<p>If you start off with y=mx+b, you end up with y=-mx+b, so reflection across the y-axis negates only the slope.</p>

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<p>azukit is perfectly correct, but I think it’s really helpful just to draw a picture and reflect it in the drawing. When you draw y=2x+5, the reflection will move the y-intercept 5 to -5, so you already know the equation is y=mx-5. Then if you look at the slope, it is the same relationship, just negative. You may get confused on the rules in some circumstances, but the drawing seems more foolproof. Try it!</p>