Question

How do you write the standard form of a line given (4,3) and (7, -2)?

Answer 1

`y=-5/3*x+29/3`

Explanation:

The slope can be computed as
`m=(y_2-y_1)/(x_2-x_1)=(-2-3)/(7-4)=-5/3`
so we get
`y=-5/3x+n`
substituting
`x=4,y=3`
we get
`3+20/3=n` so `n=29/3`

Answer 2

`5x+3y=29`

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"`

`"to begin obtain the equation in "color(blue)"slope-intercept form"`

`•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)=(4,3)" and "(x_2,y_2)=(7,-2)`

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

`y=-5/3x+blarrcolor(blue)"is the partial equation"`

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

`"using "(4,3)" then"`

`3=-20/3+brArrb=9/3+20/3=29/3`

`y=-5/3x+29/3larrcolor(red)"in slope-intercept form"`

`"multiply all terms by 3"`

`3y=-5x+29`

`"add "5x" to both sides"`

`5x+3y=29larrcolor(red)"in standard form"`

Answer 3

`color(green)(5x + 3y = 29 " is the standard form"`

Explanation:

`color(crimson)("Standard form of linear equation is " ax + by = c`

`"Given points are " (x_1, y_1) = 4,3), (x_2,y_2) = (7,-2)`

Knowing two points on a line, we can form the equation using the formula,

`(y - y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1)`

`(y - 3) / (-2 -3) = (x - 4) / (7 - 4)`

`(y - 3) / -5 = (x - 4) / 3`

`3y - 9 = -5x + 20, " cross-multiplying"`

`color(green)(5x + 3y = 29 " is the standard form"`

graph{-(5/3)x + (29/3) [-10, 10, -5, 5]}