2(-n - 3) - 7(5+ 2n)

Mathematics

1 answer:

velikii [3]3 years ago

5 0

Answer:

-16n-41

Step-by-step explanation:

2(-n-3)-7(5+2n)

Distribute

-2n-6-35-14n

Combine like terms

-16n-41

Hope this helps!

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Write the equation of the line that passes through

Gnom [1K]

Answer:

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-1, 2) and (6, 3):

$m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}$

Therefore, the slope of the line is $\frac{\displaystyle 1}{\displaystyle 7}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

Plug in one of the given points and solve for b:

$2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b$

Add $\frac{\displaystyle 1}{\displaystyle 7}$ to both sides to isolate b:

$2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b$

Therefore, the y-intercept of the line is $\frac{\displaystyle15}{\displaystyle 7}$ . Plug this back into $y=\frac{\displaystyle 1}{\displaystyle 7}x+b$ :