Question

How do you write an equation in slope-intercept form for the line that satisfies the give conditions contains (5, 7) and (-3, 11)?

Answer 1

`y=-1/2x+19/2`

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)=(5,7)" and "(x_2,y_2)=(-3,11)`

`m=(11-7)/(-3-5)=4/(-8)=-1/2`

`y=-1/2x+blarrcolor(blue)"is the partial equation"`

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

`"using "(5,7)" then"`

`7=-5/2+brArrb=14/2+5/2=19/2`

`y=-1/2x+19/2larrcolor(red)"in slope-intercept form"`