Question

A band director uses a coordinate plane to plan as how for a football game. During a show, the drummers will march along the line y=-5x-8. The trumpets players will march along a perpindicluar line that passes thorugh (-2,2). Write an equationn in slope-intercdept form for the path of the trumpet players.

Answer 1

Answer:

The equation in slope-intercept form for the path of the trumpet players is $y=\frac{x}{5}+\frac{12}{5}$.

Step-by-step explanation:

Consider the provided information.

The drummers will march along the line y=-5x-8.

The trumpets players will march along a perpendicular line that passes through (-2,2).

The slope of line y=-5x-8 is: m₁ = -5.

The slope of perpendicular lines are: $m_1\times m_2=-1$

$-5\times m_2=-1$

$m_2=\frac{1}{5}$

Hence, the slope of the line should be 1/5.

The line passes through (-2,2).

Now use point slope form to find the equation of line.

$y-y_1=m(x-x_1)$

Substitute m=1/5, x₁=-2 and y₁ = 2 in above formula.

$y-2=\frac{1}{5}(x+2)$

$y-2=\frac{x}{5}+\frac{2}{5}$

$y=\frac{x}{5}+\frac{2}{5}+2$

$y=\frac{x}{5}+\frac{12}{5}$

Hence, the equation in slope-intercept form for the path of the trumpet players is $y=\frac{x}{5}+\frac{12}{5}$.