The points 
(−1.7,2.8) and (2.5,9.94) are on the graph of a linear relationship between two variables, x and y.

To find the linear relationship (i.e., the equation of the line) between \(x\) and \(y\) passing through the points \((-1.7, 2.8)\) and \((2.5, 9.94)\), we need to find the slope (\(m\)) and the y-intercept (\(b\)) of the line in the form \(y = mx + b\).

### Step 1: Find the slope (\(m\))
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points \((-1.7, 2.8)\) and \((2.5, 9.94)\):

\[
m = \frac{9.94 - 2.8}{2.5 - (-1.7)} = \frac{7.14}{4.2} = 1.7
\]

### Step 2: Find the y-intercept (\(b\))
Now that we have the slope, we use one of the points and the slope to find the y-intercept using the equation \(y = mx + b\). We'll use the point \((-1.7, 2.8)\):

\[
2.8 = 1.7(-1.7) + b
\]

Simplifying:

\[
2.8 = -2.89 + b
\]

\[
b = 2.8 + 2.89 = 5.69
\]

### Step 3: Write the equation of the line
The equation of the line is:

\[
y = 1.7x + 5.69
\]

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What is the x-intercept of this line?
2. How would the equation change if one of the points was different?
3. How can you confirm the correctness of the equation?
4. What is the slope's interpretation in this context?
5. How would you find the distance between the two points?

**Tip**: To confirm the accuracy of a linear equation, plug both given points into the equation to verify that they satisfy it.

The points (-1.7, 2.8) and (2.5, 9.94) are on the graph of a linear relationship between two variables, x and y.

Learn how to find the equation of a line passing through the points (-1.7, 2.8) and (2.5, 9.94) using the slope-intercept form. This problem covers key algebraic concepts, including calculating the slope and determining the y-intercept. Suitable for students in Grades 8-10.

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