Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Functions
A linear function is a mathematical expression that describes a straight line when graphed. It is typically represented in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear functions is crucial for determining the relationship between variables and for solving problems involving lines.
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Slope
The slope of a line measures its steepness and direction, calculated as the change in y divided by the change in x (rise over run). For two parallel lines, the slopes are equal. In this question, the slope of the given line y = 3x + 8 is 3, which will be the same for the linear function we need to find.
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Point-Slope Form
The point-slope form of a linear equation is expressed as y - y1 = m(x - x1), where (x1, y1) is a specific point on the line and m is the slope. This form is particularly useful for writing the equation of a line when you know a point on the line and its slope, allowing for straightforward calculations in this problem.
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