Question

How do you write an equation in standard form given point (-2,5) and slope 1?

Answer 1

y = x+7

Explanation:

• Use the formula y=mx+c
  m = gradient of graph
  c= y intercept

• Substitute y,m and x in equation to find c
  `5=1*-2 +c`
  `5=-2+c`
  7=c

• Replace m and c with numbers found
  Therefore equation is y = x + 7

Answer 2

`x-y=-7`

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"`

`"begin by expressing the equation in "color(blue)"point-slope form"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`"here " m=1" and " (x_1,y_1)=(-2,5)`

`y-5=1(x-(-2))`

`rArry-5=x+2larrcolor(red)" in point-slope form"`

`"subtract y from both sides"`

`cancel(y)cancel(-y)-5=x+2-y`

`rArr-5=x+2-y`

`"subtract 2 from both sides"`

`-5-2=xcancel(+2)cancel(-2)-y`

`rArr-7=x-y " or "`

`x-y=-7larrcolor(red)" in standard form"`