Question

Which equation represents the graph
Dot 1: (0,3)
Dot 2: (5,-1)

Answer 1

To find the equation of the line that passes through the points (0, 3) and (5, -1), we can use the slope-intercept form of the equation of a line, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (0, 3)\) and \((x_2, y_2) = (5, -1)\).

Substituting the coordinates:
\[
m = \frac{-1 - 3}{5 - 0} = \frac{-4}{5}
\]

2. **Use the y-intercept (b)** from the point (0, 3). Here, \(b = 3\).

3. **Write the equation** using the calculated slope and y-intercept:
\[
y = -\frac{4}{5}x + 3
\]

Thus, the equation that represents the graph of the line through the points (0, 3) and (5, -1) is:
\[
y = -\frac{4}{5}x + 3
\]