Question

How do you write the standard form of a line given slope= 4/5, passes through (10, -3)?

Answer 1

`y=4/5x-11`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b , the y-intercept.

here `m=4/5`

Partial equation is : `y=4/5x+b`

To find b , use the point (10 ,-3) that the line passes through.

x = 10 , y = -3 and substitute into Partial equation.

`4/cancel(5)^1 xxcancel(10)^2+b=-3rArrb=-3-8=-11`

`rArrcolor(red)(|bar(ul(color(white)(a/a)color(black)(y=4/5x-11)color(white)(a/a)|)))" is the equation"`

If we multiply both sides by 5 to eliminate the fraction.

`5y=4/cancel(5)^1 xxcancel(5)^1 x-(11xx5)`

`rArr5y=x-55`

and `color(red)(|bar(ul(color(white)(a/a)color(black)(5y-x+55=0)color(white)(a/a)|)))" is another form of the equation"`