1) A linear function ? satisfies the conditionsL(−2) = 3 andL(1) = −2. a) Graph the function. b) Find an equation of the function and rite the final answer in the form L(x) = mx +b
1) A linear function ? satisfies the conditionsL(−2) = 3 andL(1) = −2. a) Graph the function. b) Find an equation of the function and rite the final answer in the form L(x) = mx +b
1) A linear function ? satisfies the conditionsL(−2) = 3 andL(1) = −2. a) Graph the function. b) Find an equation of the function and rite the final answer in the form L(x) = mx +b
ems: 1) A linear function ? satisfies the conditionsL(−2) = 3 andL(1) = −2. a) Graph the function. b) Find an equation of the function and rite the final answer in the form L(x) = mx +b.
Transcribed Image Text:### Linear Functions: Graphing and Finding the Equation
#### Problem Statement:
1) A linear function \( L \) satisfies the conditions \( L(-2) = 3 \) and \( L(1) = -2 \).
- **a) Graph the function:**
- **b) Find an equation of the function and write the final answer in the form \( L(x) = mx + b \).**
#### Instructions:
**Part a: Graphing the Function**
- On a set of coordinate axes, plot the points \((-2, 3)\) and \((1, -2)\).
- Draw a straight line through these two points, as a linear function will always create a straight line.
**Part b: Finding the Equation**
The equation of a line in slope-intercept form is given by:
\[ L(x) = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
1. **Calculate the Slope (m):**
The slope is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-2, 3)\) and \((1, -2)\):
\[
m = \frac{-2 - 3}{1 - (-2)} = \frac{-5}{3}
\]
2. **Find the y-intercept (b):**
Using the slope and one of the points, substitute into the linear equation formula to solve for \( b \).
Using point \((1, -2)\):
\[
-2 = \left( -\frac{5}{3} \right) (1) + b
\]
\[
-2 = -\frac{5}{3} + b
\]
\[
b = -2 + \frac{5}{3} = -2 + \frac{5}{3}
\]
Convert \(-2\) to a fraction with a denominator of 3:
\[
b = -\frac{6}{3} + \frac{5}{3} = -\frac{1}{3}
\]
Therefore, the equation of the linear function is:
\[ L(x) = -\frac{5}{3
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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![### Linear Functions: Graphing and Finding the Equation
#### Problem Statement:
1) A linear function \( L \) satisfies the conditions \( L(-2) = 3 \) and \( L(1) = -2 \).
- **a) Graph the function:**
- **b) Find an equation of the function and write the final answer in the form \( L(x) = mx + b \).**
#### Instructions:
**Part a: Graphing the Function**
- On a set of coordinate axes, plot the points \((-2, 3)\) and \((1, -2)\).
- Draw a straight line through these two points, as a linear function will always create a straight line.
**Part b: Finding the Equation**
The equation of a line in slope-intercept form is given by:
\[ L(x) = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
1. **Calculate the Slope (m):**
The slope is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-2, 3)\) and \((1, -2)\):
\[
m = \frac{-2 - 3}{1 - (-2)} = \frac{-5}{3}
\]
2. **Find the y-intercept (b):**
Using the slope and one of the points, substitute into the linear equation formula to solve for \( b \).
Using point \((1, -2)\):
\[
-2 = \left( -\frac{5}{3} \right) (1) + b
\]
\[
-2 = -\frac{5}{3} + b
\]
\[
b = -2 + \frac{5}{3} = -2 + \frac{5}{3}
\]
Convert \(-2\) to a fraction with a denominator of 3:
\[
b = -\frac{6}{3} + \frac{5}{3} = -\frac{1}{3}
\]
Therefore, the equation of the linear function is:
\[ L(x) = -\frac{5}{3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35d23f57-14fc-4912-bd5d-c6b1841fa652%2Feb9a42ab-1852-42f3-acf0-18e0a1e690c0%2F1c34vzv_processed.jpeg&w=3840&q=75)
