To determine the inequality represented by the graph of a line going from (0, 1) to (5, 0), we first need to find the equation of the line.
-
Determine the slope (m): The slope \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{5 - 0} = \frac{-1}{5} \]
-
Use point-slope form to find the equation of the line: We'll use one of the points, say (0, 1), in the point-slope form: \[ y - y_1 = m(x - x_1) \] Using (0, 1): \[ y - 1 = -\frac{1}{5}(x - 0) \] Simplifying this, we get: \[ y - 1 = -\frac{1}{5}x \implies y = -\frac{1}{5}x + 1 \]
-
Determine which side of the line represents the inequality:
- If the line is drawn in a way where the region above it is shaded, the inequality would be \( y > -\frac{1}{5}x + 1 \).
- If the line is drawn with the region below it shaded, the inequality would be \( y < -\frac{1}{5}x + 1 \).
-
Determine if the line is solid or dashed:
- A solid line indicates that the points on the line are included in the solution (≤ or ≥).
- A dashed line indicates that the points on the line are not included in the solution (< or >).
Assuming we do not have information about whether the line is solid or dashed or which region is shaded, we can say the equation of the line is:
\[ y = -\frac{1}{5}x + 1 \]
The inequality could be expressed generally as either:
- \( y < -\frac{1}{5}x + 1 \) (if below the line is shaded) or
- \( y > -\frac{1}{5}x + 1 \) (if above the line is shaded), depending on the graph's shading.
Please provide additional information about the shading or the line type to specify the inequality further.