So when learning about slope-intercept form, the equation that was used looked like this: $y = 2x + 3$, it then displayed a graph where the slope was going up by two and across by one. What I need a bit of clarification on is that do we just assume that the slope is, in this case, $\frac{2}{1}$, or is there something else?
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1The standard slope intercept form of an equation is given by y= mx + b, where m is the slope of the line, and (0, b) is the point at which the line crosses the y-axis, so b is also known as the y-intercept. – amWhy Sep 01 '20 at 23:15
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1So your line intersects the point $(0, 3)$ and has a slope of m = 2. Another point can be found to graph that line by going from $(0, 3),$ up two units, and over to the right one unit, to give you the second point $(0+1, 3+2) = (1, 5)$. – amWhy Sep 01 '20 at 23:17
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That part I understand but what I want to know is if given a whole number for slope, in this case, it's 2, do I just assume that it would be 2/1 in fraction form? – The Programming M16A4 Sep 01 '20 at 23:19
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1Yes, because $\frac 21 = 2$. – amWhy Sep 01 '20 at 23:21
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Ah okay! Thanks for the clarification! – The Programming M16A4 Sep 01 '20 at 23:22
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Glad to help out!! – amWhy Sep 01 '20 at 23:22
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The nice thing about slope is that if, instead of $\frac{2}{1}$, you had expressed $2$ as $\frac{4}{2}$ and drawn your line with "up $4$, over $2$", you would draw the same line. – JonathanZ Sep 01 '20 at 23:24
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That's pretty interesting! – The Programming M16A4 Sep 01 '20 at 23:57
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The standard slope intercept formula (that I was taught) is y=mx+b the variable m is your slope and the variable b is your intercept. In this case, m=2 meaning the slope is 2/1 and b=3 meaning the slope crosses the y-axis at (0,3) So, you were right when assuming the slope was 2/1. I hope this was helpful.