A line in the xy-plane is represented by the equation 3x - 4y = 24. What is the y-coordina… — SAT

A line in the $xy$ -plane is represented by the equation $3x - 4y = 24$ . What is the $y$ -coordinate of the $y$ -intercept of this line?

The

y

-coordinate of the

y

-intercept is

-6

The correct answer is

-6

. The

y

-intercept of a line is the point where it intersects the

y

-axis, which occurs when the

x

-coordinate is

0

. Substituting

x = 0

into the given equation

3x - 4y = 24

yields

-4y = 24

. Dividing both sides by

-4

gives

y = -6

Substitute

x = 0

into the equation to find the

y

-intercept.

3(0) - 4y = 24

By definition, the

y

-intercept of a line in the coordinate plane is the point where the line crosses the

y

-axis, which always has an

x

-coordinate of

0

Simplify the equation.

-4y = 24

Multiplying

3

0

yields

0

, leaving only the term containing

y

on the left side of the equation.

Solve for

y

by isolating the variable.

y = -6

Dividing both sides of the simplified equation by

-4

isolates

y

and gives the final coordinate value.

Finding the y-intercept of a linear equation in two variables by setting x = 0.

Estimated Time:45s

Question