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Question

# Find the value of y if the line through the two given points is to have the indicated slope.$( 3 , y ) \text { and } ( 1,4 ) , m = - 3$

Solution

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The slope of a line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

$\color{#4257b2}m=\dfrac{y_2-y_1}{x_2-x_1}\color{white}\tag{1}$

Let $(x_1,y_1)=(3,y)$ and $(x_2,y_2)=(1,4)$ the substitute $m=-3$:

$-3=\dfrac{4-y}{1-3}$

$-3=\dfrac{4-y}{-2}$

Multiply both sides by $-2$:

$6=4-y$

Subtract 4 from both sides:

$2=-y$

Divide both sides by $-1$:

$-2=y$

or

$\color{#c34632}y=-2$

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