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Mathematics 26 Online
eviant:

PLS HELP!! The map shows Hope Road and the construction site for the new library. Find the equation of a “street” that passes through the building site and is parallel to Hope Road.https://dlap.gradpoint.com/Resz/~yUA6AAAAAAAcCT86Gu4BdA.GdmXdvUCeIQ7vEw5T47JzB/7234256,C08/Assets/questions/quiz/algebra_1/al1paper/IMG10729x.jpg

eviant:

@demolisher1224

eviant:

@563blackghost @JustSaiyan

563blackghost:

First we need to identify the point of the library, what is the point of the library?

eviant:

7,6? or 6 1/2

563blackghost:

Yes it would be `7, 6 1/2`. Now we know that. We now need to find the equation of Hope Road. To do this we need to identify the y-intercept `(where it meets the y-axis)` and the slope `(in which we identify two points and find the slope from there)`. If we look at the graph we see that the line meets the y-axis at `6` so this is our y-intercept. \(\large\bf{y=mx+6}\) Since it passes at (0,6) we can identify another point to find the slope. Let's use (3,7). Let's plug this into slope formula... \(\Large\bf{\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \rightarrow \frac{7-6}{3-0}}\) What is the slope?

eviant:

1/3?

563blackghost:

Correct! \(\large\bf{y=\frac{1}{3}x+6}\) Now we have our equation. For the Street to be parallel the slope of it needs to be the same as Hope Road. \(\large\bf{y=\frac{1}{3}x+b}\) Now we plug the given point of the library to find the y-intercept. \(\large\bf{6 \frac{1}{2}=\frac{1}{3}(7)+b}\)

563blackghost:

With this we can find the y-intercept. Once this is found you will plug it into your equation. What is the equation?

eviant:

idk

563blackghost:

We have found that Hope Road is \(\bf{y=\frac{1}{3}x+6}\) right? Since we want the street to parallel the slope of the Street needs to be the same as Hope Road. Hope Road's slope is \(\large\bf{\frac{1}{3}}\), so the Street's slope is \(\large\bf{\frac{1}{3}}\). So we plug this into slope-intercept form. \(\large\bf{y+\frac{1}{3}x+b}\) We now need to identify the y-intercept. To do this we plug the point we are given for `the library`. \(\large\bf{6\frac{1}{2}=\frac{1}{3}(7)+b}\) What is b?

eviant:

4?

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