Mathematics: A line passing through the point (12, - 5) has a slope of 1/3. Complete the work shown. Substitute known values for m, x1, and y1. Distribute the slope through the parentheses, solve for the y variable

A line passing through the point (12, - 5) has a

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23.01.2022

The solution for the variable y is $y=\frac{1}{3} x-9$ , if a given line passing through the point (12, -5) has a slope of $\frac{1}{3}$ .

Step-by-step explanation:

The given is,

Point - (12, -5)

Slope - $\frac{1}{3}$

Step:1

Formula for slope of line,

$m = \frac{y_{2}-y_{1} } {x_{2} - x_{1} }$ ...........................(1)

Where, $(x_{1} ,y_{1} )$ , $(x_{2} ,y_{2} )$ are points

m - Slope

From given,

(12, -5) - $(x_{1} ,y_{1} )$

m = $\frac{1}{3}$

Let, (x,y ) = $(x_{2} ,y_{2} )$

Equation (1) becomes,

$\frac{1}{3} = \frac{(y - (-5))}{x-12}$

$\frac{1}{3} (x-12) = (y-(-5))$

$\frac{1}{3} (x-12) = (y+5)$

$(y+5) = \frac{1}{3} (x-12)$

$(y+5) = (\frac{1}{3} x ) -\frac{1}{3}(12))$

$(y+5) = (\frac{1}{3} x ) -4$

$y = \frac{1}{3} x -4-5$

$y = \frac{1}{3} x -9$

Result:

The solution for the variable y is $y=\frac{1}{3} x-9$ , if a given line passing through the point (12, -5) has a slope of $\frac{1}{3}$ .

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