Question

For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicular, or neither.

10x – 3y = 3
3x + 10y = 30
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of 10x - 3y = 3 is
(Type an integer or a simplified fraction.)
O B. The slope of 10x - 3y = 3 is undefined.

Answer 1

the lines are perpendicular to each other

Explanation:

The standard form of equation of a line is y = mx+c

m is the slope of the line

c is the intercept

Given the equations

10x – 3y = 3

3x + 10y = 30

Get the individual slopes

For 10x – 3y = 3

Rewrite in standard form

-3y = -10x + 3

y = 10/3 x - 3/3

y = 10/3 x - 1

Slope of the line is 10/3

For the equation 3x + 10y = 30

10y = -3x+30

y = -3/10 x + 3

Slope of the line is -3/10

Take the product of the slopes

10/3 * -3/10 = -1

Since the product of their slopes is -1, hence the lines are perpendicular to each other