Question

Given the equation Y-4=3/4(x+8) in point-slope form, identify the equation of the same line in standard form

Answer 1

3x-4y=-40

Explanation:

Hi there!

We're given the equation of the line, y-4=3/4(x+8) in point-slope form (y-
`y_(1)`=m(x-
`x_(1)`), where (
`x_(1)`,
`y_(1)`) is a point and m is the slope)

We need to convert y-4=3/4(x+8) into standard form (ax+by=c, where a, b, and c are integer coefficients; a CANNOT be 0, and CANNOT be negative).

So we need to get y-4=3/4(x+8) out of point-slope form

We can do this by converting the equation into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

to do this, we need to isolate y by itself in the equation

first, do the distributive property and distribute 3/4 on the right side

y-4=3/4x+6

add 4 to both sides

y=3/4x+10

now the equation is in slope-intercept form, but remember, we want it in standard form

x and y are on the same side in standard form, so let's subtract 3/4 x from both sides

-3/4x+y=10

however we aren't done; in standard form, the coefficients need to be integers (whole numbers), and a (the coefficient in front of x) CANNOT be negative

so let's multiply both sides by -4 to clear the fraction and change the sign of a

-4(-3/4x+y)=-4(10)

do the distributive property

3x-4y=-40

Hope this helps! :)