How do you find the missing $y$ values for a line with a slope of $-10$ which goes through $(2, 8)$ and $(3, s)$ ?

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Answer 1 · 2017-06-11T19:04:05

See a solution process below:

The slope can be found by using the formula: $m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))$

Where $m$ is the slope and ( $color(blue)(x_1, y_1)$ ) and ( $color(red)(x_2, y_2)$ ) are the two points on the line.

Substituting the slope and values from the points in the problem gives:

$-10 = (color(red)(8) - color(blue)(s))/(color(red)(2) - color(blue)(3))$

We can now solve for $s$ :

$-10 = (color(red)(8) - color(blue)(s))/-1$

$-10 = -(color(red)(8) - color(blue)(s))/1$

$-10 = -(color(red)(8) - color(blue)(s))$

$-10 = -color(red)(8) + color(blue)(s)$

$8 - 10 = 8 - color(red)(8) + color(blue)(s)$

$-2 = 0 + color(blue)(s)$

$-2 = color(blue)(s)$

$color(blue)(s) = -2$

How do you find the missing yy values for a line with a slope of -10-10 which goes through (2, 8)(2, 8) and (3, s)(3, s)?