Question

Use point-slope form to write the equation of a line that passes through the point left parenthesis, 10, comma, minus, 19, right parenthesis(10,−19) with slope minus, start fraction, 13, divided by, 9, end fraction−
9
13
​
.

Answer 1

To write the equation of a line in point-slope form, you can use the formula:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope.

Given the point \( (10, -19) \) and the slope \( m = -\frac{13}{9} \), you can substitute these values into the point-slope formula:

1. \( x_1 = 10 \)
2. \( y_1 = -19 \)
3. \( m = -\frac{13}{9} \)

Now substitute these into the formula:

\[
y - (-19) = -\frac{13}{9}(x - 10)
\]

This simplifies to:

\[
y + 19 = -\frac{13}{9}(x - 10)
\]

So, the equation of the line in point-slope form is:

\[
y + 19 = -\frac{13}{9}(x - 10)
\]