Determine the intercept of the line 4x - 1 = 3y + 5.

4x - 1 = 3y + 5

slope: 4/3

y-intercept: - 2

To find the x-intercept, substitute in 0 for y and solve for x.

4 x - 1 = 3 (0) + 5

Solve the equation.

x = 3 / 2

To find the y-intercept, substitute in 0 for x and solve for y.

4 (0) - 1 = 3 y + 5

Solve the equation.

Rewrite the equation as 3 y + 5 = 4 (0) - 1.

3 y + 5 = 4 (0) - 1

Simplify the right side.

Multiply 4 by 0.

3 y + 5 = 0 - 1

Subtract 1 from 0.

3 y + 5 = - 1.

Move all terms not containing y to the right side of the equation.

Subtract 5 from both sides of the equation.

3 y = - 5 - 1

Subtract 1 from - 5.

3 y = - 6

Divide each term by 3 and simplify.

Divide each term in 3 y = - 6 by 3.

3 y / 3 = - 6 / 3

Reduce the expression by cancelling the common factors.

y = - 6 / 3

Simplify the right side of the equation.

y = - 2

These are the x and y intercepts of the equation 4 x - 1 = 3 y + 5.

x-intercept: (3 / 2, 0)

y-intercept: (0, - 2)