Question

What is equation of the line in standard form that passes through (2, 7) and ( -4, 1)?

Answer 1

`y = mx + b`

`y = x+5`

`x-y=-5`

Explanation:

First, find the slope of the equation using

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (1-7)/(-4-2)`

`m = 1`

Second, plug in m (the slope) into the equation `y = mx +b`

So it becomes `y = 1x + b`

Plug in one of the points into the `x and y` values into the equation above and solve for `b.`

So, `(7) = 1(2) + b`

`b = 5`

Finally, plug in the `b` value into the equation to get the standard form equation.

`y = x+5" "larr` re-arrange

`x-y=-5`

Answer 2

`x-y=-5`

Explanation:

`"the equation of a line in "color(blue)"standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))`

`"where A is a positive integer and B, C are integers"`

`"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(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(2,7)" and "(x_2,y_2)=(-4,1)`

`rArrm=(1-7)/(-4-2)=(-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 "(2,7)" then"`

`7=2+brArrb=7-2=5`

`rArry=x+5larrcolor(red)"in slope-intercept form"`

`rArrx-y=-5larrcolor(red)"in standard form"`