For the equation -4y =8x, what is the constant of variation?
a: -4
b: -2
c: 1
d: 2
what is an equation for the line with slope 2/3 and y-intercept 9?
a: y=2/3x
b: y= 9x
c: y= 2/3x + 9
d: y= 9x + 2/3
what is an equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1)?
a: y= 3x + 1
b: y= x - 3
c: y= 2x + 5
d: y= 2x - 5

1) Option b is correct, constant of variation is -2.

2) Option c is correct, Equation of line is

3)Option d is correct, equation of line in a slope-intercept form is, y=2x -5

Step-by-step explanation:

1)

Direct variation states that a relationship between the two variables. we say y varies directly as x

i.e, or y =kx.................[1] ;  where k is the constant of variation.

Given the equation:

Divide both sides by -4 we get;

Simplify:

            .......[2]

On comparing equation [2] with [1] we get;

k = -2

Therefore, the constant of variation is -2

2)

Equation of line is in the form of y =mx +b where m is the slope of the line and b is the y-intercepts.

Given: slope(m)= and y-intercept(b) = 9

Substitute in the equation of line we get;

therefore, the equation of line is,

3)

Slope intercept form: For any two point and , the equation of line is given by:

or

y= mx + b ; where m is the slope given by

and y-intercept

Given the points (1 , -3) and (3, 1) ;

Then, the equation of line is:

or

Simplify:

Using distributive property i.e,

y+3 = 2x -2

Subtract 3 from both sides we get;

y+3-3=2x-2-3

Simplify:

y = 2x - 5.

Therefore, the equation of line in a slope-intercept form is y=2x -5

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