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Write the equation of the line that passes through (-8,-4) and (-6,-1) in slope-intercept form.

User Pursuit
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Answer:

To find the equation of the line passing through the points (-8,-4) and (-6,-1), we first need to find the slope (\(m\)) of the line using the formula:

\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]

Let's use the points (-8,-4) and (-6,-1):

\[m = \frac{{-1 - (-4)}}{{-6 - (-8)}} = \frac{{3}}{{2}}\]

Next, we'll use the point-slope form of a linear equation, which is:

\[y - y_1 = m(x - x_1)\]

We'll choose one of the points to substitute, let's use (-8,-4):

\[y - (-4) = \frac{{3}}{{2}}(x - (-8))\]

Simplify the equation:

\[y + 4 = \frac{{3}}{{2}}(x + 8)\]

Multiply both sides by 2 to eliminate the fraction:

\[2y + 8 = 3(x + 8)\]

Distribute the 3:

\[2y + 8 = 3x + 24\]

Now, isolate \(y\):

\[2y = 3x + 16\]

\[y = \frac{{3x + 16}}{{2}}\]

So, the equation of the line in slope-intercept form is \(y = \frac{{3x + 16}}{{2}}\).

Explanation:

User Suvartheec
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