Find an equation for the graph that has points (-2,1) and (4,5)

To find the equation of the line that passes through the points \((-2, 1)\) and \( (4, 5)\), we can use the point-slope form of a linear equation. The steps are as follows:

### 1. Find the Slope (\(m\)):
The slope \(m\) of the line can be calculated using the formula:

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

Substituting the given points \((x_1, y_1) = (-2, 1)\) and \((x_2, y_2) = (4, 5)\):

\[
m = \frac{5 - 1}{4 - (-2)} = \frac{4}{6} = \frac{2}{3}
\]

### 2. Use the Point-Slope Form:
The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

Using the slope \(m = \frac{2}{3}\) and one of the points, say \((-2, 1)\):

\[
y - 1 = \frac{2}{3}(x + 2)
\]

### 3. Simplify to Slope-Intercept Form:
Now, we'll simplify this equation to the slope-intercept form \(y = mx + b\):

\[
y - 1 = \frac{2}{3}(x + 2)
\]
\[
y - 1 = \frac{2}{3}x + \frac{4}{3}
\]
\[
y = \frac{2}{3}x + \frac{4}{3} + 1
\]
\[
y = \frac{2}{3}x + \frac{4}{3} + \frac{3}{3}
\]
\[
y = \frac{2}{3}x + \frac{7}{3}
\]

### Final Equation:
The equation of the line that passes through the points \((-2, 1)\) and \((4, 5)\) is:

\[
y = \frac{2}{3}x + \frac{7}{3}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the equation of a line passing through the points \((1, 2)\) and \((3, 4)\)?
2. How do you find the equation of a line given a point and a slope?
3. What is the slope of the line passing through the points \((0, 0)\) and \((5, 10)\)?
4. How can you determine if two lines are parallel using their slopes?
5. What is the slope-intercept form of a line with a slope of \(-2\) passing through the point \((1, 3)\)?

**Tip:** When finding the equation of a line from two points, always calculate the slope first, then use one of the points to find the y-intercept.

Learn how to find the equation of a line passing through the points (-2, 1) and (4, 5) using the point-slope form and slope-intercept form. This problem covers fundamental concepts in linear equations and is suitable for students in Grades 7-9.

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