Graphing Equations and Inequalities

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Questions and Answers

What is the slope of the line represented by the equation $4x - 5y = -25$?

$-4/5$
$-5/4$
$4/5$ (correct)
$5/4$

What is the shaded region for the inequality $y < -x - 2$ when graphed?

Below the line with y-intercept -2 (correct)
Below the x-axis
Above the x-axis
Above the line with y-intercept -2

Which transformation occurs in the function $y = |x + 4| - 1$ compared to the parent function $y = |x|$?

Shift right by 4 and up by 1
Shift right by 4 and down by 1
Shift left by 4 and down by 1 (correct)
Shift left by 4 and up by 1

What is the vertex of the graph of the function $y = -|x-4| + 2$?

<p>(4, 2) (D)</p> Signup and view all the answers

For the equation $4x - 5y = -25$, what is the y-intercept?

<p>5 (D)</p> Signup and view all the answers

Flashcards

Graphing Linear Equations

A line on a coordinate plane representing all the points that satisfy the equation. Example: 4x - 5y = -25.

Graphing Equations

A visual representation of the relationship between two variables, typically on a coordinate plane, showing solutions to an equation.

Graphing Absolute Value Functions

A V-shaped graph with a pointed vertex that represents all points that satisfy the absolute value function. Example: y = |x + 4| - 1.

Vertex

A point on a graph where the line or curve changes direction. For absolute value functions, it's the pointed bottom of the 'V'.

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Graphing Inequalities

A solution to an inequality is a point on the coordinate plane that satisfies the inequality. The shaded region on a graph represents all the solutions.

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Study Notes

Graphing Equations and Inequalities

Equation 1: 4x – 5y = -25
- Graph a straight line
- Find the x-intercept (set y = 0)
- Find the y-intercept (set x = 0)
Equation 2: y < -x - 2
- Graph a dashed line for the inequality y = -x - 2
- Shade the region below the line, as y is less than -x - 2.
Equation 3: y = |x + 4| - 1
- Vertex at (-4, -1)
- Graph a "V" shape
- Graph the equation y = |x +4| first
- Shift down by 1 for y = |x +4| -1.
Equation 4: y = -|x-4| + 2
- Graph a "V" shape that opens downward
- Vertex is at (4, 2)
- Reflect with a negative sign (-|x–4|)
- Translate up by 2 for y = -|x-4| + 2