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

Question

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

0

1. ## 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
)