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2 months ago

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Line AB passes through points A(−6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y=mx+b, the

n m=m equals negative StartFraction 1 Over 6 EndFraction.. What is the value of b?

2 answers:

babunello [11.8K]2 months ago

5 0

Answer:

$m=-\frac{1}{6}$

$b=5$

Step-by-step explanation:

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-6,\:6\right),\:\left(x_2,\:y_2\right)=\left(12,\:3\right)$

$m=\frac{3-6}{12-\left(-6\right)}$

$m=-\frac{1}{6}$

The equation can be expressed in point-slope format

$y-y_1=m\left(x-x_1\right)$

In this case:

m represents the slope and

$\left(x_1,\:y_1\right)$ is a specific point on the line

using $m=-\frac{1}{6}$ and $\left(x_1,\:y_1\right)=\left(-6,\:6\right)$ then

$y-6=-\frac{1}{6}\left(x-\left(-6\right)\right)$

$-\frac{1}{6}\left(x-\left(-6\right)\right)=y-6$

$\mathrm{Multiply\:both\:sides\:by\:}-6$

$\left(-\frac{1}{6}\left(x-\left(-6\right)\right)\right)\left(-6\right)=y\left(-6\right)-6\left(-6\right)$

$x+6=-6y+36$

$x+6-36=-6y$

$x-30=-6y$

$\frac{x-30}{-6}=\frac{-6y}{-6}\:$

$y=\frac{-1}{6}x+5$

Consequently

$y=\frac{-1}{6}x+5$

by equating the expression with the slope-intercept format

$y=mx+b$

thus,

$y=mx+b$

$y=\frac{-1}{6}x+5$

<pin conclusion="">

$m=-\frac{1}{6}$

$b=5$

</pin>

Svet_ta [12.7K]2 months ago

4 0

Answer:

it's essentially c.5

Step-by-step explanation:

refer to the information above

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