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#
Which equation runs through points (1, 6) and (-1, 2)?

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Question:

A
\(y = 2x + 4\)

explanation

Slope, *m*, is defined as rise over run, or the vertical distance between two points divided by the horizontal distance between the same points:

\(m= \frac{\mathrm{rise} }{\mathrm{sun}} = \frac{\mathrm{( y_2-y_1 )} }{\mathrm{(x_2-x_1)}} \), where \((x_1, y_1)\) and \((x_2,y_2)\) are two points along the line.

To compute for *m* in the problem use \((x_1, y_1) = (-1;2)\) and \((x_2,y_2)= (1;6)\)

\(m= \frac{\mathrm{6-2} }{\mathrm{1-(-1)} } = \frac{\mathrm{4} }{\mathrm{2}}=2\)

The straight-line equation in the slope-intercept form applies, that is:

\(y = mx + b\), where *m* is the slope and *b* is the value of *y* when *x* = 0 (the *y*-intercept)

Initially, we know that the equation will be something like this:

\(y = 2x + b\)

Since there is only one choice that fits this description, save time by choosing that answer.

However, if there were more than one choices that fit the description, or if it isn't a multiple choice problem, continue:

We need to know *b*, which we compute by plugging in either of the points given:

If we use (x, y)=(-1, 2):

\(y = 2x + b\)

\(2 = 2(-1) + b\)

\(2 = -2 + b\)

\(2 + 2 = b\)

\(4 = b\)

Therefore, the correct equation is:

\(y = 2x + 4\)

TIP: you can check by using the other given point, (1, 6).

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