# How do you write the equation in slope intercept form given (3,4) with slope 1/4?

Jun 26, 2016

Same solution as Pluma but with a little bit more explanation.

$y = \frac{1}{4} x + \frac{13}{4}$

#### Explanation:

Let the given point be ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(3 , 4\right)$

Let any other unknown point on the line be ${P}_{2} \to \left(x , y\right)$

Then the gradient $m = \left(\text{change in y")/("change in x}\right) \to \frac{y - {y}_{1}}{x - {x}_{1}}$

Giving $\text{ } \textcolor{b r o w n}{m = \frac{1}{4} = \frac{y - 4}{x - 3}}$
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Multiply both sides by $4 \left(x - 3\right)$

 color(brown)(" "1/4xx4(x-3)" "=" "(y-4)/(x-3)xx4(x-3))

 color(brown)(" "4/4xx(x-3)" "=" "4(y-4)xx(x-3)/(x-3))

But $\frac{4}{4} = 1 \mathmr{and} \frac{x - 3}{x - 3} = 1 \text{ giving:}$

 color(brown)(" "x-3=4(y-4)" "->" "x-3=4y-16)

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 color(brown)(" "x-3+16=4y+0" "->" "x+13=4y)
 color(brown)(" "1/4x+13/4=y)
 color(brown)(" "y=1/4x+13/4)