Final answer:
To graph the linear function g(x) = -4x + 7x, combine like terms to get g(x) = 3x, plot the origin, and use the slope of 3 to find another point. Draw a straight line through the points to represent the function.
Step-by-step explanation:
The student has asked to graph the linear function g(x)= -4x+7x. First, combine like terms in the equation. The equation simplifies to g(x) = 3x. This is a linear function without a y-intercept, which means the line will pass through the origin (0,0). To graph this function, you can plot the origin and then use the slope, which is 3, to find another point. Since the slope is 3 (or 3/1), you can go up 3 units and right 1 unit from the origin to reach the point (1,3). Plot this second point and then draw a straight line through both points, extending in both directions. This is the graph of g(x) = 3x, which shows the dependence of y on x and indicates a direct relationship between the two variables.