Question
upstudy study bank question image url

What is the slope of the line that passes through the points \( (1,-9) \) and \( (4,-7) \) ? Write your answer in simplest form.

Ask by Conner Hanson. in the United States
Feb 21,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The slope of the line is \( \frac{2}{3} \).

Solution

To find the slope \( m \) of the line that passes through the points \( (x_1, y_1) = (1, -9) \) and \( (x_2, y_2) = (4, -7) \), we can use the formula for the slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Now, substituting the values of the points into the formula: \[ m = \frac{-7 - (-9)}{4 - 1} \] Let's simplify this step by step: 1. Calculate the numerator: \[ -7 - (-9) = -7 + 9 = 2 \] 2. Calculate the denominator: \[ 4 - 1 = 3 \] Now, substituting these results back into the slope formula: \[ m = \frac{2}{3} \] Thus, the slope of the line that passes through the points \( (1, -9) \) and \( (4, -7) \) is \[ \frac{2}{3} \] in simplest form.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

The Deep Dive

To find the slope of the line that passes through the points \( (1,-9) \) and \( (4,-7) \), you can use the formula for slope, \( m \), which is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (1, -9) \) and \( (x_2, y_2) = (4, -7) \). Plugging in the values: \[ m = \frac{-7 - (-9)}{4 - 1} = \frac{-7 + 9}{3} = \frac{2}{3} \] So, the slope of the line is \( \frac{2}{3} \). Now, let's spice things up a bit! Picture yellow umbrellas at the beach! The slope, like the rise and the run of those umbrellas in the sand, tells us how steep they are leaning. A slope of \( \frac{2}{3} \) means that for every 3 units you move to the right (run), you'll go up 2 units (rise) – like walking up a gentle hill towards ice cream! Also, getting practical with this concept, if you're ever frustrated solving a problem involving slopes, just remember: ensure you align your points correctly on a graph and double-check your calculations. It’s easy to mix up your coordinates! Take it step-by-step, and soon enough, you’ll be the slope guru of any math gathering.

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • 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

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy