What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21?

3x - y = 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + 3y = 21 ( subtract x from both sides )

3y = - x + 21 ( divide all terms by 3 )

y = - x + 7 ← in slope- intercept form

with slope m = -

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = 3 , thus

y = 3x + c ← is the partial equation

To find c , substitute (1, - 3) into the partial equation

- 3 = 3 + c ⇒ c = - 3 - 3 = - 6

y = 3x - 6 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 6 ( add 6 to both sides )

6 = 3x - y , that is

3x - y = 6 ← in standard form

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.