Textbook Question
Graph each function. See Examples 6–8. g(x) = ½ x³ - 4
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0. Review of College Algebra
Basics of Graphing
1:40 minutesProblem 2
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The point (4, ________) lies on the graph of the equation y = 3x - 6.
Verified step by step guidance1
Identify the given equation of the line: \(y = 3x - 6\).
Recognize that the point has an x-coordinate of 4, so substitute \(x = 4\) into the equation to find the corresponding y-coordinate.
Substitute \(x = 4\) into the equation: \(y = 3 \times 4 - 6\).
Simplify the right-hand side: \(y = 12 - 6\).
Calculate the value of \(y\) to find the missing coordinate of the point.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Understanding Linear Equations
A linear equation like y = 3x - 6 represents a straight line on the coordinate plane. Each x-value corresponds to exactly one y-value, determined by substituting x into the equation. Recognizing this helps find missing coordinates on the line.
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Coordinate Points on a Graph
A point on a graph is represented as (x, y), where x is the horizontal position and y is the vertical position. To verify if a point lies on a graph, substitute the x-value into the equation and check if the resulting y matches the point's y-coordinate.
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Substitution Method for Finding Coordinates
To find a missing coordinate, substitute the known x-value into the equation and solve for y. This method directly uses the equation to determine the corresponding y-value, ensuring the point lies on the graph.
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