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Charra [1.4K]
2 years ago
6

Find the slope of the line y= -1/3x-6

Mathematics
1 answer:
Diano4ka-milaya [45]2 years ago
6 0

Answer:

-1/3

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept.

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Read 2 more answers
How do i find the slope
Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

<u>m=</u>\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }<u></u>

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show <u>rise</u>, over the difference in the x points to show <u>run</u>.

Now, to find the slope we insert our values, starting with our second y point:

<u>m=</u>\frac{2-y_{1 } }{x_{2} -x_{1} }<u></u>

Now insert our first y point:

<u>m=</u>\frac{2-4 }{x_{2} -x_{1} }<u></u>

Now we insert our second x point:

<u>m=</u>\frac{2-4 }{-3 -x_{1} }<u></u>

And finally our first x point:

<u>m=</u>\frac{2-4 }{-3 -3 }

Now, we solve:

<u>m=</u>\frac{-2 }{-6}

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

<u>m=</u>\frac{2 }{6}

Now, we simplify our fraction by dividing the top and bottom by 2:

<u>m=</u>\frac{1}{3}<u></u>

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y=\frac{1}{3}x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

<u>m=</u>\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }<u></u>

Insert our values:

<u>m=</u>\frac{4-1}{2-(-4)}<u></u>

Get rid of the double negative:

<u>m=</u>\frac{4-1}{2+4}<u></u>

Solve:

<u>m=</u>\frac{3}{6}<u></u>

Simplify:

<u>m=</u>\frac{1}{2}

Now that we know our slope, let's plug it in to our slope intercept form equation.

y=\frac{1}{2}x+3

I hope this was helpful! Keep learning! :D

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