Consider the line that passes through the point $$ \mathrm{P}(4,5) $$ and has slope -2 . Write the slope-intercept form of the equation of the line. Use exact values.

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To find the slope-intercept form of the equation of a line, we can use the formula:

$$
y = mx + b
$$

where $$ m $$ is the slope and $$ b $$ is the y-intercept.

Given:
- The slope $$ m = -2 $$
- The point $$ P(4, 5) $$

We can substitute the slope and the coordinates of point $$ P $$ into the equation to find $$ b $$.

1. Substitute $$ m $$, $$ x $$, and $$ y $$ into the equation:
   $$
   5 = -2(4) + b
   $$

2. Calculate $$ -2(4) $$:
   $$
   -2(4) = -8
   $$

3. Substitute this value back into the equation:
   $$
   5 = -8 + b
   $$

4. Solve for $$ b $$:
   $$
   b = 5 + 8 = 13
   $$

Now we have both $$ m $$ and $$ b $$:
- Slope $$ m = -2 $$
- Y-intercept $$ b = 13 $$

Thus, the slope-intercept form of the equation of the line is:

$$
y = -2x + 13
$$
The equation of the line in slope-intercept form is $$ y = -2x + 13 $$.

Consider the line that passes through the point \( \mathrm{P}(4,5) \) and has slope -2 . Write the slope-intercept form of the equation of the line. Use exact values.

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