1. State the points before you start working. For example: "My points are ( $$ 1 \mathrm{p}, 1 $$ ) and ( 4 , 10)." 2. Compute the slope, m , using the slope formula. If you compute a decimal, make sure to convertitto a fraction, so it is an exact answer. 3. Use the pointeslope form of a line to create the equation of the line going through the two points. If you have a special case of a line that is not a function, then just write the equation of the line and explain why you can't use the point-slope formula. 4. If possible, put the line in slope-intercept form and identify the y-intercept value as an ordered pair. Again, for those with special cases, give the equation of the line and the x-intercept. 5. Use Deamos or Craphmatica to graph your line. Adjust the axes so the $$ y $$-intercept is shown and labeled. If your line does not have ay-intercept, still graph it, show and label the $$ x $$-intercept, and explain why, in terms of grophing, it is not a function.

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**Step 1. State the Points**

My points are $$ (1, 1) $$ and $$ (4, 10) $$.

**Step 2. Compute the Slope**

The slope $$ m $$ is calculated using the formula

$$
m = \frac{y_2 - y_1}{x_2 - x_1}.
$$

Substitute the given points:

$$
m = \frac{10 - 1}{4 - 1} = \frac{9}{3} = 3.
$$

The slope of the line is $$ 3 $$.

**Step 3. Write the Equation Using Point-Slope Form**

The point-slope form of a line is:

$$
y - y_1 = m(x - x_1).
$$

Using the point $$ (1, 1) $$ and $$ m = 3 $$:

$$
y - 1 = 3(x - 1).
$$

**Step 4. Convert to Slope-Intercept Form and Identify the $$ y $$-Intercept**

Solve the equation $$ y - 1 = 3(x - 1) $$ for $$ y $$:

$$
y - 1 = 3x - 3,
$$
$$
y = 3x - 3 + 1,
$$
$$
y = 3x - 2.
$$

The slope-intercept form is $$ y = 3x - 2 $$.

The $$ y $$-intercept is the point where $$ x = 0 $$:

$$
y = 3(0) - 2 = -2.
$$

Thus, the $$ y $$-intercept as an ordered pair is $$ (0, -2) $$.

**Step 5. Graphing the Line**

Using graphing software such as Deamos or Craphmatica, you can plot the line $$ y = 3x - 2 $$. Make sure to:

- Adjust the $$ y $$-axis so that the $$ y $$-intercept $$ (0, -2) $$ is shown and clearly labeled.
- Plot the points $$ (1, 1) $$ and $$ (4, 10) $$ along with the $$ y $$-intercept $$ (0, -2) $$.
- Draw the straight line through these points.

Since the line has a well-defined $$ y $$-intercept and passes the vertical line test, it is a function.

**Points:** $$ (1, 1) $$ and $$ (4, 10) $$ **Slope ($$ m $$):** 3 **Point-Slope Form:** $$ y - 1 = 3(x - 1) $$ **Slope-Intercept Form:** $$ y = 3x - 2 $$ with $$ y $$-intercept at $$ (0, -2) $$ **Graph:** A straight line passing through $$ (1, 1) $$, $$ (4, 10) $$, and $$ (0, -2) $$. It is a function.

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