Question 54977
Write the equation of the line that passes through the points (x1,y1)=(3,5) and (x2,y2)=(-1,10)
:
We need a slope (m) and a point to make the equation of a line:
If we have two points, (x1,y1) and (x2,y2) we can find the slope with the slope formula:{{{highlight(m=(y2-y1)/(x2-x1))}}}
{{{m=(10-5)/(-1-3)}}}
{{{m=5/-4}}}
:
Now that we have a slope to go with a point we can use the point-slope formula {{{highlight(y-y1=m(x-x1))}}}, where m=slope and (x1,y1) is a given point, to make an equation of a line:
{{{y-5=(-5/4)(x-3)}}}
{{{4(y-5)=4(-5/4)(x-3)}}}
{{{4y-20=(-20/4)(x-3)}}}
{{{4y-20=-5(x-3)}}}
{{{4y-20=-5x+15}}}
{{{4y-20+20=-5x+15+20}}}
{{{4y=-5x+35}}}
{{{4y/4=-5x/4+35/4}}}
{{{highlight(y=(-5/4)x+35/4)}}}
Happy Calculating!!!