Question

Write the equation of line and slope intercept form using the coordinates (1,-4) (0,1)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) using the given coordinates (1, -4) and (0, 1), we first need to calculate the slope (m).

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

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

Using the points (1, -4) as \((x_1, y_1)\) and (0, 1) as \((x_2, y_2)\):

\[
m = \frac{1 - (-4)}{0 - 1} = \frac{1 + 4}{0 - 1} = \frac{5}{-1} = -5
\]

Now that we have the slope \( m = -5 \), we can use one of the points to find the y-intercept \( b \). We'll use the point (0, 1), which is particularly useful since it already represents the y-intercept.

In the slope-intercept form, the equation is:

\[
y = mx + b
\]

Substituting \( m = -5 \) and \( b = 1 \):

\[
y = -5x + 1
\]

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

\[
y = -5x + 1
\]