Question

How do you write an equation of a line that passes through (-5, 9) and (1,3)?

Answer 1

`y=-x+4`

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)=(-5,9)" and "(x_2,y_2)=(1,3)`

`rArrm=(3-9)/(1-(-5))=(-6)/6=-1`

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

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

`"using "(1,3)" then"`

`3=-1+brArrb=3+1=4`

`rArry=-x+4larrcolor(red)"in slope-intercept form"`