Write the equation of the line that passes through the points (1, 1) and (2, 4).  Write your answer in slope-intercept form.


To find the equation of the line that passes through the points \((1, 1)\) and \((2, 4)\), we'll use the slope-intercept form, which is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

**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 \((1, 1)\) and \((2, 4)\):

\[
m = \frac{4 - 1}{2 - 1} = \frac{3}{1} = 3
\]

**Step 2: Use the slope to find the y-intercept (\(b\)).**

Using the slope-intercept form \(y = mx + b\), plug in the slope \(m = 3\) and one of the points, say \((1, 1)\):

\[
1 = 3 \cdot 1 + b
\]

Solving for \(b\):

\[
1 = 3 + b \implies b = 1 - 3 = -2
\]

**Step 3: Write the final equation.**

Substituting \(m = 3\) and \(b = -2\) into the slope-intercept form:

\[
y = 3x - 2
\]

So, the equation of the line in slope-intercept form is:

\[
\boxed{y = 3x - 2}
\]

Would you like more details, or do you have any questions?

Here are some related questions you might find useful:

1. How do you find the equation of a line given a slope and a point?
2. What is the significance of the y-intercept in the slope-intercept form?
3. How can you convert an equation from slope-intercept form to standard form?
4. How do you determine if two lines are parallel or perpendicular?
5. What is the point-slope form of a line, and when is it useful?

**Tip:** Always double-check your calculations when finding slopes and intercepts to avoid simple arithmetic errors!

Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form.

Learn how to find the equation of the line passing through the points (1, 1) and (2, 4) in slope-intercept form. This problem covers key algebraic concepts like slope calculation and using the slope-intercept form to determine the equation of a line. Suitable for students in Grades 8-10.

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