Question

How do you write an equation of a line given A(8,11) and B(14,5)?

Answer 1

`y=-x+19`

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 the slope m use the "color(blue)"gradient formula"`

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

`"let "(x_1,y_1)=(8,11)" and "(x_2,y_2)=(14,5)`

`rArrm=(5-11)/(14-8)=(-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 "(8,11)" then"`

`rArr11=-8+brArrb=11+8=19`

`rArry=-x+19" is the equation of the line"`