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Your classmate Juan missed the lesson on graphing linear equations using slope-intercept form. You attend the class and what to help Juan understand the material he missed. Assume Juan knows how to graph $y=x$.

Part A: Write an explanation for Juan that describes the y-intercept of a line and what happens to the graph of $y=x$ as you change the y-intercept. Be specific and consider several cases.

Part B: Write an explanation for Juan that describes the slope $m$ of a line and what happens to the graph of $y=x$ as you change the slope. Be specific and consider several cases.

well here it it seems hard right... well it does to me , I really don't know what to do

Robert Howard
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aaly b
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1 Answers1

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$y=x$ is a line passing through origin, with a slope of $1$.

Part:A

Here we are just changing the y-intercept, so the slope remains same. So if we keep on changing the y-intercept, we get lines which are parallel to $y=x$.

All the lines with a positive y-intercept lie to the left of the line $y=x$, i.e., in the second quadrant.

Part:B

Here we are just changing the slope of the line $y=x$. So in general let the slope be $m$. Since the line still passes through origin, because we are only changing the slope, the equation of the new line would be $y=mx$.

To get a more clear understanding of this, just take a pen hold it firmly at the center and rotate it in any which direction you want. The same thing happens in in Part:B.

lsp
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