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Questions and Answers
What is the slope of the line represented by the equation $4x - 5y = -25$?
What is the slope of the line represented by the equation $4x - 5y = -25$?
What is the shaded region for the inequality $y < -x - 2$ when graphed?
What is the shaded region for the inequality $y < -x - 2$ when graphed?
Which transformation occurs in the function $y = |x + 4| - 1$ compared to the parent function $y = |x|$?
Which transformation occurs in the function $y = |x + 4| - 1$ compared to the parent function $y = |x|$?
What is the vertex of the graph of the function $y = -|x-4| + 2$?
What is the vertex of the graph of the function $y = -|x-4| + 2$?
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For the equation $4x - 5y = -25$, what is the y-intercept?
For the equation $4x - 5y = -25$, what is the y-intercept?
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Study Notes
Graphing Equations and Inequalities
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Equation 1: 4x – 5y = -25
- Graph a straight line
- Find the x-intercept (set y = 0)
- Find the y-intercept (set x = 0)
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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.
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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.
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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
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Description
This quiz covers graphing various types of equations and inequalities, including linear equations and absolute value functions. You will need to identify intercepts, graph lines, and shade regions for inequalities. It's a practical way to test your understanding of graphing techniques.
