1. State the points before you start working. For example: "My points are $$ (10,1) $$ and (4,10). 2. Compute the slope, $$ m $$, using the slope formula. If you compute a decimal, make sure to convert it to afraction, so it is an exact answer. 3. Use the point-slope 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, glve the equation of the line and the $$ x $$-intercept. 5. Use Desmos or Graphmatica to graph your Unc. Adjust the axce so the y-Intercept is shown and labeled. If your line does not have a y-intercept, still graph it, show and tabel the x-Intercept, and explain why, in terms of graphing, it is not a function.

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**1. State the points:**  
My points are $$ (10,1) $$ and $$ (4,10) $$.

**2. Compute the slope $$ m $$:**  
The slope formula is  
$$
m = \frac{y_2 - y_1}{x_2 - x_1}.
$$  
Substitute the points into the formula:  
$$
m = \frac{10 - 1}{4 - 10} = \frac{9}{-6} = -\frac{3}{2}.
$$

**3. Use the point-slope form to create the equation of the line:**  
The point-slope form of a line is  
$$
y - y_1 = m(x - x_1).
$$  
Using the point $$ (10,1) $$ and the slope $$ -\frac{3}{2} $$:  
$$
y - 1 = -\frac{3}{2}(x - 10).
$$

**4. Put the line in slope-intercept form and identify the y-intercept:**  
First, distribute the slope:  
$$
y - 1 = -\frac{3}{2}x + \frac{3}{2} \times 10.
$$  
Simplify the constant term:  
$$
\frac{3}{2} \times 10 = 15.
$$  
So the equation becomes:  
$$
y - 1 = -\frac{3}{2}x + 15.
$$  
Add 1 to both sides:  
$$
y = -\frac{3}{2}x + 16.
$$  
The slope-intercept form is  
$$
y = -\frac{3}{2}x + 16.
$$  
The y-intercept is when $$ x = 0 $$; thus, the y-intercept is  
$$
(0,16).
$$

**5. Graphing using Desmos or Graphmatica:**  
Plot the line $$ y = -\frac{3}{2}x + 16 $$ on a graphing tool (such as Desmos). Ensure that the y-intercept $$ (0,16) $$ is clearly shown and labeled. You will see that the line crosses the y-axis at $$ (0,16) $$.  
The graph verifies that the line is a function because for every value of $$ x $$ there is exactly one value of $$ y $$.
**1. Points:** $$ (10,1) $$ and $$ (4,10) $$. **2. Slope $$ m $$:** $$ m = -\frac{3}{2} $$ **3. Equation of the line:** $$ y - 1 = -\frac{3}{2}(x - 10) $$ **4. Slope-intercept form and y-intercept:** $$ y = -\frac{3}{2}x + 16 $$ Y-intercept: $$ (0,16) $$ **5. Graphing:** The line $$ y = -\frac{3}{2}x + 16 $$ is graphed with the y-intercept at $$ (0,16) $$. It is a function since each $$ x $$ has one corresponding $$ y $$.

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