Question

How do you find the equation of the line passing through the points (1,4) and (-2,6)?

Answer 1

`y=-2/3x+14/3`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(1,4)" and "(x_2,y_2)=(-2,6)`

`rArrm=(6-4)/(-2-1)=2/(-3)=-2/3`

`rArry=-2/3x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute either of the 2 given points into"`
`"the partial equation"`

`"using "(1,4)" then"`

`4=-2/3+brArrb=12/3+2/3=14/3`

`rArry=-2/3x+14/3larrcolor(red)"equation of line"`