Question

A coordinate plane with a line passing through the points (negative 4, negative 5) and (1, negative 1).Write an equation in standard form of the line that is graphed. Then find the x- and y-intercepts.The equation of the line in standard form is .The x-intercept is .The y-intercept is .



The equation of the line in standard form is
4x-5y=9?
5x-4y=9?
4x-5y=-1?

The x-intercept is
-9/5
1/5
9/4

The y-intercept is
-9/5
9/4
-5/4

Answer 1

To find the equation of the line in standard form that passes through the points \((-4, -5)\) and \((1, -1)\), we first calculate the slope of the line.

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the values of our points:

\[
m = \frac{-1 - (-5)}{1 - (-4)} = \frac{-1 + 5}{1 + 4} = \frac{4}{5}
\]

Thus, the slope of the line is \(\frac{4}{5}\).

Next, we will use the point-slope form of the equation of a line which is:

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

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

\[
y - (-5) = \frac{4}{5}(x - (-4))
\]

This simplifies to:

\[
y + 5 = \frac{4}{5}(x + 4)
\]

Distributing the right side:

\[
y + 5 = \frac{4}{5}x + \frac{16}{5}
\]

To isolate \(y\), we subtract 5 from both sides:

\[
y = \frac{4}{5}x + \frac{16}{5} - 5
\]

Since \(5\) can be written as \(\frac{25}{5}\):

\[
y = \frac{4}{5}x + \frac{16}{5} - \frac{25}{5}
\]

This gives:

\[
y = \frac{4}{5}x - \frac{9}{5}
\]

Now we will convert this into standard form \(Ax + By = C\). To eliminate the fraction, we can multiply the entire equation by 5:

\[
5y = 4x - 9
\]

Rearranging gives:

\[
-4x + 5y = -9
\]

To write it in standard form \(Ax + By = C\) with \(A\) positive, we multiply through by \(-1\):

\[
4x - 5y = 9
\]

So the equation of the line in standard form is:

**4x - 5y = 9**

Next, we find the x-intercept and y-intercept.

### X-Intercept:
To find the x-intercept, set \(y = 0\):

\[
4x - 5(0) = 9 \implies 4x = 9 \implies x = \frac{9}{4}
\]

### Y-Intercept:
To find the y-intercept, set \(x = 0\):

\[
4(0) - 5y = 9 \implies -5y = 9 \implies y = -\frac{9}{5}
\]

### Summary:
The equation of the line in standard form is **4x - 5y = 9**.
The x-intercept is \(\frac{9}{4}\).
The y-intercept is \(-\frac{9}{5}\).

So to finalize:

- The equation of the line in standard form is **4x - 5y = 9**.
- The x-intercept is **\(\frac{9}{4}\)**.
- The y-intercept is **\(-\frac{9}{5}\)**.