Question

Which equation represents the function graphed on the coordinate plane?

A. g(x)=(x+4−2)
B. g(x)=(x−4−2)
C. g(x)=5x−2
D. g(x)=(x−2+4)

Answer 1

Option B, g(x) = (x - 4 - 2), represents the function graphed on the coordinate plane.

Step-by-step 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.

Answer 2

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.

Step-by-step 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.