Final answer:
The correct answer is option A: It makes the line become steeper. In linear equations such as y = mx + b, the coefficient in front of x (also known as the slope or m) determines the steepness of the line.
Step-by-step explanation:
The correct answer is that increasing the value of the coefficient in front of x in a linear equation makes the line become steeper. This is seen in the steepness of the lines on the graph as the coefficient increases.
A larger coefficient means that for every unit increase in x, y increases by a greater amount, resulting in a steeper line. This is evident in the comparison of equations y1, y2, and y3; as the coefficient of x increases, the lines represented by these equations become steeper on the graph. Therefore, increasing the value of the coefficient in front of x does not move the line up or down on the coordinate plane (option C and option D are incorrect) nor does it make the line shallower (eliminating option B).
Increasing the value of the coefficient in front of x, also known as the slope, affects the steepness of the line. A larger slope means the line becomes steeper, while a smaller slope makes the line shallower. The slope represents the rate of change between the x and y coordinates. So, increasing the slope will result in a greater change in the y-coordinate for each unit increase in the x-coordinate.