Answer:
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
