At the halftime show, a marching band marched in formation. the lead drummer started at a point with coordinates (-2, -5) and moved 3 steps up and 1 step right. a. write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?

Part a) The rule of the translation is (x,y) > (x+1,y+3)

Part b) The coordinates of the drummer's final position are (-1,-2)

Step-by-step explanation:

Part a) Write a rule to describe the translation

we know that

The lead drummer moved 3 steps up and 1 step right.

so

3 steps up > that means (y+3)

1 step right ---> that means (x+1)

The rule of the translation is equal to

(x,y) > (x+1,y+3)

Part b) What were the coordinates of the drummer's final position?

we know that

The drummer's initial position is the point (-2,-5)

Applying the rule of the translation

(x,y) > (x+1,y+3)

(-2,-5) > (-2+1,-5+3)

(-2,-5) > (-1,-2)

therefore

The coordinates of the drummer's final position are (-1,-2)

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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 ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form