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Answer :
Final answer:
The equation that represents the function graphed on the coordinate plane is g(x) = (x - 4 - 2). When a linear equation is written in the form y = mx + b, 'm' represents the slope of the line and 'b' represents the y-intercept. In this case, the equation has a slope of 1 and a y-intercept of -6.
Explanation:
The equation that represents the function graphed on the coordinate plane is g(x) = (x - 4 - 2).
When a linear equation is written in the form y = mx + b, 'm' represents the slope of the line and 'b' represents the y-intercept, which is the point where the line intersects the y-axis.
In this case, the equation g(x) = (x - 4 - 2) has a slope of 1 (since the coefficient of 'x' is 1) and a y-intercept of -6 (since the constant term is -6). This means that the graph of this equation is a line that passes through the point (0, -6) and has a slope of 1.
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Final answer:
Option B, g(x) = (x - 4 - 2), represents the function graphed on the coordinate plane.
Explanation:
The equation that represents the function graphed on the coordinate plane is g(x) = (x - 4 - 2), which is option B.
To determine the equation of a linear function from a graph, we need to identify the slope and y-intercept. In this case, the line intersects the y-axis at -2 (y-intercept) and has a slope of 1 (rise of 1 on the vertical axis for every increase of 1 on the horizontal axis). Therefore, the equation can be written as y = mx + b, where m is the slope and b is the y-intercept.
Option B, g(x) = (x - 4 - 2), is the only equation that matches the characteristics of the graph described and represents a linear function.
