PLEASE HELP!!!

Find the slope for the following line: y = 3/4 x – 7 (1 point)

–7

7

3/4

-4/3

What is the y-intercept of the graph of the line given by the equation 3y + 4x = 15? (1 point)

5

4

3

–4/3

Solve the system of equations by substitution.

x = –4y

x + 5y = 2 (1 point)

(–8, 2)

(8, –2)

(2/9, –8/9)

(–12, 3)

Solve the system of equations by elimination.

3x + 4y = 31

2x – 4y = –6 (1 point)

(4, 5)

(5, 4)

(–5, 12.5)

(5, –4)

The simplification of given equation can be carried out by using slope intercept form and also by using the arithmetic operations.

1).

Given :

\(y = \dfrac{3}{4}x-7\) --- (1)

To determine the slope of the given line, slope intercept form can be use and the slope intercept form is given by:

\(y = mx+c\) --- (2)

Now, compare both the equation (1) and (2), we get the slope of the line \(y = \dfrac{3}{4}x-7\) that is, \(m = \dfrac{3}{4}\) .

2).

Given :

3y + 4x = 15

Further simplify the given equation.

\(y = \dfrac{-4x+15}{3}=\dfrac{-4}{3}x+5\) ----- (3)

To determine the y-intercept of the given line, slope intercept form can be use and the slope intercept form is given by:

\(y = mx+c\) --- (4)

Now, compare both the equation (3) and (4), we get the y-intercept of the line \(y = \dfrac{-4}{3}x+5\) that is, \(c = 5\).

3).

Given :

\(x = -4y\) ---- (5)

\(x+5y = 2\) ---- (6)

Now, substitute the value of 'y' given in equation (5) in equation (6).

\(-4y+5y=2\)

\(y = 2\)

Now, put the value of y in equation (5).

\(x = -4\times2\)

\(x = -8\)

Therefore, the correct option is A).

4).

Given :

3x + 4y = 31 ---- (7)

2x - 4y = -6 ---- (8)

Further simplify the equation (7).

\(x = \dfrac{31-4y}{3}\) --- (9)

Now, put the value of x given in equation (9) in equation (8).

\(2\times\left[\dfrac{31-4y}{3}\right]-4y=-6\)

\(62-8y-12y=-18\)

62 - 20y = -18

80 = 20y

y = 4

Put the value of y in equation (9) we get:

x = 5

Therefore, the correct option is B).

For more information, refer the link given below:

https://brainly.com/question/2263981