
Graph the line with slope 1 passing through the point (-5,2).

To graph the line with slope \(1\) passing through the point \((-5, 2)\), we use the point-slope form of a line equation:

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

where:
- \(m = 1\) is the slope,
- \((x_1, y_1) = (-5, 2)\) is the given point.

Substitute the values into the equation:

\[
y - 2 = 1(x - (-5)) \implies y - 2 = x + 5
\]

Now, solving for \(y\):

\[
y = x + 5 + 2 \implies y = x + 7
\]

So, the equation of the line is:

\[
y = x + 7
\]

This line has a slope of \(1\) and passes through \((-5, 2)\). To graph the line, you can plot the point \((-5, 2)\), then use the slope to find another point. Since the slope is \(1\), for every unit you move to the right, you move up by \(1\).

Let me know if you would like me to graph this for you or explain further!

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Here are five related questions for further exploration:
1. How would the graph change if the slope was \(2\) instead of \(1\)?
2. What is the y-intercept of the line \(y = x + 7\)?
3. How would you write the equation of a line with slope \(-1\) passing through \((0, 3)\)?
4. How do you determine the slope from two points on a line?
5. How can you graph a line parallel to \(y = x + 7\)?

**Tip**: When using the point-slope form, it's often easier to write the equation of a line if you know the slope and a single point.

Graph the line with slope 1 passing through the point (-5,2).

Learn how to graph the line with a slope of 1 passing through the point (-5, 2). This problem covers key algebraic concepts, including the point-slope form of a linear equation and its transformation to slope-intercept form. Suitable for students in Grades 7-9.

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