Question

What is the equation of the line passing through `(3,4)` and `(4,2)`?

Answer 1

`y=-2x+10`

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)=(3,4)" and "(x_2,y_2)=(4,2)`

`m=(2-4)/(4-3)=(-2)/1=-2`

`y=-2x+blarrcolor(blue)"is the partial equation"`

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

`"using "(4,2)" then"`

`2=-8+brArrb=2+8=10`

`y=-2x+10larrcolor(red)"is the equation of line"`