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# Coordinates

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The graph of a function is a line that passes through the points (3, 17) and (6, 32). What is the equation of this function?

Jun 9, 2021

#1
+1

My math is very rusty, admittedly, so perhaps I shouldn't pick back up the keyboard to help, but I still will regardless. If I recall, this is going to be a point-slope formula problem, followed by a slope-intercept formula problem.

Point slope formula: $$y − y_{1} = m(x − x_{1})$$

Substitute the values accordingly: Treat $$(3, 17)$$ as $$y$$ and $$(6, 32)$$ as $$y_{1}$$.

Post-substitution: $$17 - 32 = m(3 - 6)$$

From there, simplify as needed.

Step 1: $$17 - 32 = m(3 - 6)$$

Step 2: $$-15 = m(-3)$$

Step 3: $$\frac{-15}{-3} = \frac{m(-3)}{-3}$$

Step 4: $$5 = m$$

From there, take either point and, knowing the value of $$y$$$$m$$, and $$x$$, plug in those numbers to the slope intercept formula to find $$b$$ and make sure they match.

Slope intercept formula: $$y=mx+b$$

Substitutions: $$17=5(3)+b$$ and $$32=5(6)+b$$

Calculations 1: $$17=15+b$$ and $$32=30+b$$

Calculations 2: $$(17-15)=(15-15)+b$$ and $$(32-30)=(30-30)+b$$

Solution(s): $$2=b$$ for both equations.

The likely solution is that your answer wants to be done up in slope-intercept form, in which case you would plug in your values for $$m$$ and $$b$$, which would yield a final answer of $$y=5x+2$$. Hope this helped with understanding how you reached such an answer!

Jun 9, 2021
#2
+2

WELCOME BACK GOLDENLEAF! I do this in a way that is not quite mathematically correct but it works fine.

$$\frac{rise}{run}=\frac{rise}{run}\\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\ \frac{y-17}{x-3}=\frac{32-17}{6-3}\\$$

and then just simply

Technically this presentation is not quite right because it would make a hole at x=3, but just ignore that.

Jun 9, 2021
edited by Melody  Jun 9, 2021
#3
+1

Good to be back! Albeit only on rare occasion, since I'm not in school anymore (had to drop out due to finances). And I haven't taken a maths course (to completion) since... gosh, 2016? But I'll still be here to keep my mind sharp, and to stay learned!

GoldenLeaf  Jun 12, 2021