What is an equation of the line that passes through the point (-1, -3) and is
parallel to the line 4x – y = 2?

y = 4x + 1

Step-by-step explanation:

1. Solve given equation for y

4x-y=2

4x=y+2

y=4x-2

2. Parallel in linear equations means the new line will have the same slope, so your new equation so far is

y=4x+b      (formula being used is linear function y=mx+b)

3. (-1,-3) is a coordinate (x,y), so plug those values in for x and y so the only variable in your equation is b, the y-intercept

-3=4(-1)+b     Solve for b

-3=-4+b

1=b

4. Rewrite your new equation with the m and b you now know

y=4x+1

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is