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.