given the following system of equations and their graph below, what can be determined about the slopes and y-intercepts of the system of equations?

(graph)
4x + 2y = −2
x − 3y = 24

the slopes are different, and the y-intercepts are different.
the slopes are different, and the y-intercepts are the same.
the slopes are the same, and the y-intercepts are different.
the slopes are the same, and the y-intercepts are the same.

  The slopes are different, and the y-intercepts are different

Step-by-step explanation:

The lines on the graph are not parallel, so the slopes are different.

The lines on the graph intersect the y-axis in different places, so the y-intercepts are different.

Step-by-step explanation:

Parallel lines have the same slope.

The lines are not parallel, therefore have the different slopes.

y-intercepts are different (look at the picture)

-1 and -8.

The slope-ntercept form of an equation of a line:

m - slope

b - y-intercept

We have the equations of a lines in the standard form (Ax + By = C).

Convert ot the slope-intercept form:

        subtract 4x from both sides

          divide both sides by 2

Therefore we have the slope m = -2, and the y-intercept b = -1.

            subtract x from both sides

        divide both sides by (-3)

Therefore we have the slope m = 1/3, and the y-intercept b = -8.

-2 ≠ 1/3 and -1 ≠ -8

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b