Question

How do you write an equation of a line given `(-5,-2),(5,2)`?

Answer 1

`y=2/5x`

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)=(-5,-2)" and "(x_2,y_2)=(5,2)`

`m=(2-(-2))/(5-(-5))=4/10=2/5`

`y=2/5x+blarrcolor(blue)"is the partial equation"`

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

`"using "(5,2)" then"`

`2=2+brArrb=2-2=0`

`y=2/5xlarrcolor(red)"is the equation of the line"`