QuestionFind the equation in point-slope form for a line through $(4,4)$ with slope $-\frac{5}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the point $(4,4)$ . The slope of the line is $-\frac{5}{}$
3. We want to find the equation of the line in point-slope form, which is $y - y1 = m(x - x1)$ where $(x1, y1)$ is a point on the line and $m$ is the slope of the line.

STEP 2

We can start by writing down the general form of the point-slope equation, which is $y - y1 = m(x - x1)$ .

STEP 3

Now, we can substitute the given point $(,)$ into the equation. This point will be our $(x1, y1)$ .
$y - = m(x -)$

STEP 4

Next, we substitute the given slope $-\frac{}{2}$ for $m$ in the equation.
$y -4 = -\frac{}{2}(x -4)$

STEP 5

This is the equation of the line in point-slope form.
$y -4 = -\frac{5}{2}(x -4)$ So, the equation of the line that passes through the point $(4,4)$ and has a slope of $-\frac{5}{2}$ is $y -4 = -\frac{5}{2}(x -4)$ .

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