Hurry 30 pts what is the equation of the graphed line written in standard form? a. 3x + y = –5 b. x + 3y = –5 c. 3x – 5y = –15 d. 5x – 3y = 15

D

the equation of a line in slope- intercept form is

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 ) = (3, 0 ) and (x₂, y₂ ) = (0, - 5 )

m = =

line crosses y-axis at (0, - 5 ) hence c = - 5

y = x - 5 ← in slope-intercept form

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearrange slope-intercept form into standard form

multiply all terms by 3

3y = 5x - 15 ( subtract 3y and add 15 to both sides )

5x - 3y = 15 ← in standard form → D

9

step-by-step explanation:

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