Consider the given graph. +
-2
2
4
U
Which equation represents this direct variation?
y =-3/2x
y =-2/3x
y = -2x
y = -x

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: