Find an equation for the line that passes through the point (-3,7) and is perpendicular to 3x-5y=80. give your answer in point-slope form. show as much work as possible to support your answer.

y-7=-(5/3)(x+3)

Step-by-step explanation:

step 1

Find the slope of the line that is perpendicular to 3x-5y=80

we have

3x-5y=80

5y=3x-80

y=(3/5)x-16

The slope of the given line is m1=3/5

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

m1*m2=-1

Find m2

(3/5)*m2=-1

m2=-5/3

step 2

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-5/3

point (-3,7)

substitute

y-7=-(5/3)(x+3) > equation of the line into point slope form

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point