Powell Reid
11/05/2023 · Senior High School

Find \( f ( x ) \) if \( f \) is a linear function that has the given properties. \( f ( - 1 ) = 1 , f ( 4 ) = 21 \) \( f ( x ) = \square \) (Simplify your answer.) 

Real Tutor Solution

Tutor-Verified Answer

Quick Answer

Your input: find the equation of a line given two points \( P = ( - 1,1 ) \) and \( Q = ( 4,21 ) \) 

The slope of a line passing through the two points \( P = ( x _ { 1 } , y _ { 1 } ) \) and \( Q = ( x _ { 2 } , y _ { 2 } ) \) is given by \( m = \frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } \) 

We have that \( x _ { 1 } = - 1 , y _ { 1 } = 1 , x _ { 2 } = 4 , y _ { 2 } = 21 \) 

Plug the given values into the formula for slope: \( m = \frac { ( 21 ) - ( 1 ) } { ( 4 ) - ( - 1 ) } = \frac { 20 } { 5 } = 4\) 

Now, the \( y \) -intercept is \( b = y _ { 1 } - m \cdot x _ { 1 } \) (or \( b = y _ { 2 } - m \cdot x _ { 2 } \) , the result is the same). 

\( b = 1 - ( 4 ) \cdot ( - 1 ) = 5\) 

Finally, the equation of the line can be written in the form \( y = m x + b \) . 

\( y = 4 x + 5 \) . 

The slope of the line is \( m = 4 \) 

The equation of the line in the slope-intercept form is \( y = 4 x + 5 \) . 

The equation of the line in the point-slope form is \( y - 1 = 4 ( x + 1 ) \) . 

The equation of the line in the point-slope form is \( y - 21 = 4 ( x - 4 ) \) . 

The general equation of the line is \( 4 x - y + 5 = 0 \) . 

Reviewed and approved by the UpStudy tutoring team
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text

Enter your question here…

By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
📸 STUDY CAN BE A REAL STRUGGLE
Why Not UpStudy It?
Select your plan below
Premium

You can enjoy

  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to answer and
    solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic
  • Limited Solutions