Find the equation of the line that passes through left parenthesis 46 comma 345 right parenthesis and left parenthesis 64 comma 390 right parenthesis in​ slope-intercept form.
yequals
select: 2.5x+230
2.5 x plus 230                                                                                                                                                                        Use the linear equation you found  to predict the number of calories in a candy bar that weighs 52.8 grams.

### Step 1: Find the equation of the line in slope-intercept form

The general form for a line is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line
- \( b \) is the y-intercept

#### 1.1 Find the slope \( m \)

The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (46, 345) \) and \( (64, 390) \):

\[
m = \frac{390 - 345}{64 - 46} = \frac{45}{18} = 2.5
\]

#### 1.2 Find the y-intercept \( b \)

Now that we know the slope is \( m = 2.5 \), we can substitute one of the points into the slope-intercept form to find \( b \). Let's use \( (46, 345) \):

\[
345 = 2.5(46) + b
\]
\[
345 = 115 + b
\]
\[
b = 345 - 115 = 230
\]

So, the equation of the line is:

\[
y = 2.5x + 230
\]

### Step 2: Predict the number of calories in a candy bar weighing 52.8 grams

Substitute \( x = 52.8 \) into the equation \( y = 2.5x + 230 \):

\[
y = 2.5(52.8) + 230 = 132 + 230 = 362
\]

Thus, a candy bar weighing 52.8 grams is predicted to contain 362 calories.

---

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you calculate the slope if the points are reversed?
2. What is the significance of the slope in the context of this problem?
3. How would the equation change if the y-intercept were different?
4. Can this equation be used to predict calorie content for any weight of candy bars?
5. How can you verify the accuracy of this model?

**Tip:** The slope \( m \) in a linear equation tells you how much \( y \) changes for each unit increase in \( x \).

Find the equation of the line that passes through (46, 345) and (64, 390) in slope-intercept form. Use the linear equation you found to predict the number of calories in a candy bar that weighs 52.8 grams.

Learn how to find the equation of a line that passes through two points (46, 345) and (64, 390) in slope-intercept form. Use the linear equation to predict the number of calories in a candy bar weighing 52.8 grams. This problem explores concepts in algebra and linear equations, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation