Question

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

Answer 1

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

`y=1/4x+13/4`

Explanation:

Let the given point be `P_1->(x_1,y_1)->(3,4)`

Let any other unknown point on the line be `P_2->(x,y)`

Then the gradient `m=("change in y")/("change in x")->(y-y_1)/(x-x_1)`

Giving `" "color(brown)(m=1/4=(y-4)/(x-3))`
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Multiply both sides by `4(x-3)`

# 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 `4/4=1 and (x-3)/(x-3)=1" giving:"`

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

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Add 16 to both sides

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

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Divide both sides by 4

# color(brown)(" "1/4x+13/4=y)#

# color(brown)(" "y=1/4x+13/4)#