What is the equation of a line, in slope-intercept form, that connects the following two data points?

(5.0, 1300)

(6.0, -850)

Enter your answer by filling in the following blanks. Enter each of your answers as whole numbers without any rounding.



To find the equation of the line in slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

### Step 1: Calculate the slope \( m \)
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Substitute the given points \( (5.0, 1300) \) and \( (6.0, -850) \):

\[
m = \frac{-850 - 1300}{6.0 - 5.0} = \frac{-2150}{1} = -2150
\]

So, the slope \( m = -2150 \).

### Step 2: Use the slope-intercept form
Now, we can use the slope-intercept form \( y = mx + b \), where \( m = -2150 \), to find \( b \).

### Step 3: Solve for the y-intercept \( b \)
Substitute one of the points, say \( (5.0, 1300) \), into the equation \( y = mx + b \):

\[
1300 = -2150(5.0) + b
\]

\[
1300 = -10750 + b
\]

\[
b = 1300 + 10750 = 12050
\]

### Final Equation
The equation of the line is:

\[
y = -2150x + 12050
\]

Would you like any further details or clarification on this?

Here are 5 questions that expand on this concept:
1. How would the equation change if the points were reversed?
2. What does the slope of -2150 indicate about the direction of the line?
3. How would you interpret the y-intercept of 12050 in this context?
4. Can you find the x-intercept of this line?
5. How would the equation change if the slope were zero?

**Tip:** In slope-intercept form, the slope tells you the steepness and direction of the line, while the y-intercept indicates where the line crosses the y-axis.

What is the equation of a line, in slope-intercept form, that connects the following two data points? (5.0, 1300) (6.0, -850)

Learn how to find the equation of a line in slope-intercept form that connects two data points: (5.0, 1300) and (6.0, -850). This algebra problem covers concepts such as slope calculation and using the slope-intercept formula. Suitable for students in Grades 8-10.

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