Question

graphing linear inequality systems
aurora sarabia
graphing liinear inequality systems (a.rei.12)
systems of linear inequalities
system of linear inequalities

y = -3x + 6

y = x + 2

one solution:
(1,3)

y > -3x + 6

y ≤ x + 2

y = 2x + 6

y = 2x - 1

no solution
2y = -2x + 8
y = -x + 4

infinite
solutions
a.rei.12
school
open-ended question
what are two ways that graphing a linear inequality is different than graphing a linear
equation?
hint: consider how the actual inequality sign indicates some of these differences.
type your answer here

Explanation:

1. Line Style: For a linear equation (e.g., \( y = mx + b \)), we graph a solid line (since all points on the line are solutions). For a linear inequality, if the inequality is strict (\( > \) or \( < \)), we use a dashed line (points on the line are not solutions); if it's non - strict (\( \geq \) or \( \leq \)), we use a solid line.
2. Solution Region: A linear equation has a line as its graph (only the points on the line are solutions). A linear inequality has a region of the coordinate plane as its solution set. We shade the region that satisfies the inequality. For example, for \( y > - 3x + 6 \), we shade the area above the line \( y=-3x + 6 \) (and the line is dashed), while for \( y=-3x + 6 \), only the points on the line are solutions.

Answer:

1. When graphing a linear equation, we use a solid line (all points on the line are solutions), while for a linear inequality, we use a dashed line for strict inequalities (\(>\) or \(<\)) (points on the line are not solutions) and a solid line for non - strict inequalities (\(\geq\) or \(\leq\)).
2. A linear equation's graph is just the line (only points on the line are solutions), but a linear inequality's graph includes a shaded region (all points in the region satisfy the inequality).