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 $(x_1,y_1)$ and $(x_2,y_2)$ is
$m = (y_2 - y_1)/(x_2 - x_1)$

For the given values $(x_1,y_1) = (5,8)$ and $(x_2,y_2) = (10,14)$
we have
$m = (14- 8)/(10-5) = 6/5$

Using (arbitrarily) $(x_1,y_1) = (5,8)$ as a point
and (not arbitrarily) $m=6/5$ as the slope

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

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

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

$y = 6/5x + 2$

The slope is $6/5$ and the y-intercept is $2$