Question 90895


If you want to find the equation of line with a given a slope of {{{2}}} which goes through the point ({{{6}}},{{{4}}}), you can simply use the point-slope formula to find the equation:



---Point-Slope Formula---
{{{y-y[1]=m(x-x[1])}}} where m is the slope, and ({{{x[1]}}},{{{y[1]}}}) is the given point


So lets use the Point-Slope Formula to find the equation of the line


{{{y-4=(2)(x-6)}}} Plug in {{{m=2}}}, {{{x[1]=6}}}, and {{{y[1]=4}}} (these values are given)


{{{y-4=(2)x-(2)(6))}}} Distribute {{{2}}}


{{{y-4=(2)x+(-2)(6))}}} Multiply the negatives


{{{y-4=(2)x+-12}}} Multiply {{{-2}}} and {{{6}}} to get {{{-12}}}


{{{y=(2)x+-12+4}}}Add {{{4}}} to both sides


{{{y=2x-8}}} Combine like terms

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Answer:



So the equation of the line with a slope of {{{2}}} which goes through the point ({{{6}}},{{{4}}}) is:


{{{y=2x-8}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=2}}} and the y-intercept is {{{b=-8}}}


Notice if we graph the equation {{{y=2x-8}}} and plot the point ({{{6}}},{{{4}}}),  we get (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{drawing(500, 500, -3, 15, -5, 13,
graph(500, 500, -3, 15, -5, 13,(2)x+-8),
circle(6,4,0.12),
circle(6,4,0.12+0.03)
) }}} Graph of {{{y=2x-8}}} through the point ({{{6}}},{{{4}}})

and we can see that the point lies on the line. Since we know the equation has a slope of {{{2}}} and goes through the point ({{{6}}},{{{4}}}), this verifies our answer.