Tutorial Exercise Find an equation of the line passing through the pair of points. Sketch the line. $$ (5,4),(-5,-5) $$ Step 1 Compute the slope of the line. $$ \square $$

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To find the equation of the line passing through the points $$(5, 4)$$ and $$(-5, -5)$$, we will first compute the slope of the line.

### Step 1: Compute the slope of the line

The formula for the slope $$m$$ of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:

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

Here, we can assign:
- $$(x_1, y_1) = (5, 4)$$
- $$(x_2, y_2) = (-5, -5)$$

Now, substituting these values into the slope formula:

$$
m = \frac{-5 - 4}{-5 - 5}
$$

Calculating the numerator and denominator:

$$
m = \frac{-9}{-10} = \frac{9}{10}
$$

So, the slope of the line is $$m = \frac{9}{10}$$.

### Step 2: Find the equation of the line

We can use the point-slope form of the equation of a line, which is:

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

Using the point $$(5, 4)$$ and the slope $$m = \frac{9}{10}$$:

$$
y - 4 = \frac{9}{10}(x - 5)
$$

Now, we can simplify this equation to the slope-intercept form $$y = mx + b$$.

### Step 3: Simplify the equation

Distributing the slope on the right side:

$$
y - 4 = \frac{9}{10}x - \frac{9}{10} \cdot 5
$$

Calculating $$-\frac{9}{10} \cdot 5$$:

$$
-\frac{9}{10} \cdot 5 = -\frac{45}{10} = -4.5
$$

Now, substituting this back into the equation:

$$
y - 4 = \frac{9}{10}x - 4.5
$$

Adding 4 to both sides:

$$
y = \frac{9}{10}x - 4.5 + 4
$$

Calculating $$-4.5 + 4$$:

$$
-4.5 + 4 = -0.5
$$

Thus, the equation of the line is:

$$
y = \frac{9}{10}x - 0.5
$$

### Step 4: Sketch the line

To sketch the line, we can plot the two points $$(5, 4)$$ and $$(-5, -5)$$ and draw a line through them. The slope indicates that for every 10 units moved horizontally to the right, the line rises 9 units vertically.

Now, let's summarize the findings:
- Slope $$m = \frac{9}{10}$$
- Equation of the line: $$y = \frac{9}{10}x - 0.5$$

If you would like me to plot the line, please let me know!
The slope of the line is $$ \frac{9}{10} $$, and the equation of the line passing through the points $$(5, 4)$$ and $$(-5, -5)$$ is $$ y = \frac{9}{10}x - 0.5 $$.

Tutorial Exercise Find an equation of the line passing through the pair of points. Sketch the line. \[ (5,4),(-5,-5) \] Step 1 Compute the slope of the line. \( \square \)

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