-3
Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y
=
m
x
+
b
, where m is the slope and b is the y intercept.
y
=
m
x
+
b
Find the values of m and b using the form y
=
m
x
+
b
.
m
=−
5
3
b
=
2
The slope of the line is the value of m
, and the y-intercept is the value of b
.
Slope:
−
5
3
y-intercept: 2
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f
(
0
)
=
−
5
(
0
)
3
+
2
Simplify the result.
Simplify each term.
Cancel the common factor of 0 and 3
.
Factor 3 out of 5
(
0
)
.
f
(
0
)
=
−
3
(
5
⋅
(
0
)
)
3
+
2
Cancel the common factors.
Factor 3 out of 3
.
f
(
0
)
=
−
3
(
5
⋅
(
0
)
)
3
(
1
)
+
2
Cancel the common factor.
f
(
0
)
=
−
3
(
5
⋅
(
0
)
)
3
⋅
1
+
2
Rewrite the expression.
f
(
0
)
=
−
5
⋅
(
0
)
1
+
2
Divide 5
⋅
(
0
) by 1
.
f
(
0
)
=
−
(
5
⋅
(
0
)
)
+
2
Multiply 5 by 0
.
f
(
0
)
=
−
0
+
2
Multiply −
1 by 0
.
f
(
0
)
=
0
+
2
Add 0 and 2
.
f
(
0
)
=
2
The final answer is 2
.
2
The y value at x
=
0 is 2
.
y
=
2
Choose 3 to substitute in for x to find the ordered pair.
Replace the variable x with 3 in the expression.
f
(
3
)
=
−
5
(
3
)
3
+
2
Simplify the result.
Simplify each term.
Cancel the common factor of 3
.
Cancel the common factor.
f
(
3
)
=
−
5
⋅
3
3
+
2
Divide 5 by 1
.
f
(
3
)
=
−
1
⋅
5
+
2
Multiply −
1 by 5
.
f
(
3
) = -5 +2
Add −
5 and 2
.
f
(
3
)
=
−
3
The final answer is −
3
.
−
3
The y value at x
=
3 is −
3
.
y
=
−
3
Create a table of the x and y values.
x-
0, 3
y- 2, -3
Graph the line using the slope and the y-intercept, or the points.
Slope: −
5
/3
y-intercept: 2
x- 0, 3
y- 2, -3
