Question

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

Answer 1

Answer:

• $m=-\frac{1}{6}$

• $b=5$

Step-by-step explanation:

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

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

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

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

As the equation in  point-slope form

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

Here:

• m is the slope and

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

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

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

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

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

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

$x+6=-6y+36$

$x+6-36=-6y$

$x-30=-6y$

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

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

Thus

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

comparing the equation with the slope-intercept form

$y=mx+b$

so,

$y=mx+b$

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

Therefore,

• $m=-\frac{1}{6}$

• $b=5$

Answer 2

A general line equation is something of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

We will find that the value of b is 5.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be written as:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Here we do know that the line passes through (-6, 6) and (12, 3).

Then the slope is just:

$m = \frac{3 - 6}{12 - (-6)} = -\frac{1}{6}$

Then the linear equation is something like:

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

Now, knowing that the function passes through the point (-6, 6), we can replace these values in the above equation to get:

$6 = -\frac{1}{6}*-6 + b\\\\6 = 1 + b\\\\6 - 1 = b = 5$

Then the linear equation is:

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

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