How would you find y=mx+b when given (5,8) and (10, 14)?

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How would you find y=mx+b when given (5,8) and (10, 14)?

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Answer 1 · 2015-04-07T20:03:43

In general, the slope of a line joining points $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ is
$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2 - y_1)/(x_2 - x_1)$

For the given values $(x_{1}, y_{1}) = (5, 8)$ $(x_1,y_1) = (5,8)$ and $(x_{2}, y_{2}) = (10, 14)$ $(x_2,y_2) = (10,14)$
we have
$m = \frac{14 - 8}{10 - 5} = \frac{6}{5}$ $m = (14- 8)/(10-5) = 6/5$

Using (arbitrarily) $(x_{1}, y_{1}) = (5, 8)$ $(x_1,y_1) = (5,8)$ as a point
and (not arbitrarily) $m = \frac{6}{5}$ $m=6/5$ as the slope

The slope-point formula for the line can be written as
$(y - 8) = \frac{6}{5} (x - 5)$ $(y-8) = 6/5(x-5)$

$\to 5 y - 40 = 6 x - 30$ $rarr 5y - 40 = 6x - 30$
$\to 5 y = 6 x + 10$ $rarr 5y = 6x +10$

We can convert this to slope-intercept form $y = m x + b$ $y=mx+b$
by dividing both sides by $5$ $5$

$y = \frac{6}{5} x + 2$ $y = 6/5x + 2$

The slope is $\frac{6}{5}$ $6/5$ and the y-intercept is $2$ $2$

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How would you find y=mx+b when given (5,8) and (10, 14)?

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