timmy writes the equation ( f(x)=\frac{1}{4}x - 1 ). he then doubles both of the terms on the right side to…

timmy writes the equation ( f(x)=\frac{1}{4}x - 1 ). he then doubles both of the terms on the right side to create the equation ( g(x)=\frac{1}{2}x - 2 ). how does the graph of ( g(x) ) compare to the graph of ( f(x) )?\nthe line of ( g(x) ) is steeper and has a higher ( y )-intercept.\nthe line of ( g(x) ) is less steep and has a lower ( y )-intercept.\nthe line of ( g(x) ) is steeper and has a lower ( y )-intercept.\nthe line of ( g(x) ) is less steep and has a higher ( y )-intercept.

timmy writes the equation ( f(x)=\frac{1}{4}x - 1 ). he then doubles both of the terms on the right side to create the equation ( g(x)=\frac{1}{2}x - 2 ). how does the graph of ( g(x) ) compare to the graph of ( f(x) )?\nthe line of ( g(x) ) is steeper and has a higher ( y )-intercept.\nthe line of ( g(x) ) is less steep and has a lower ( y )-intercept.\nthe line of ( g(x) ) is steeper and has a lower ( y )-intercept.\nthe line of ( g(x) ) is less steep and has a higher ( y )-intercept.

Answer

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is (y = mx + b), where (m) is the slope and (b) is the (y) - intercept. For (f(x)=\frac{1}{4}x - 1), (m_f=\frac{1}{4}) and (b_f=-1). For (g(x)=\frac{1}{2}x - 2), (m_g=\frac{1}{2}) and (b_g=-2).

Step2: Compare the slopes

The slope (m) determines the steepness of the line. If (|m_1|>|m_2|), the line with slope (m_1) is steeper. Since (\frac{1}{2}>\frac{1}{4}) (because (\frac{1}{2}=\frac{2}{4})), the line (g(x)) is steeper than (f(x)).

Step3: Compare the (y) - intercepts

The (y) - intercept (b) is the value of (y) when (x = 0). We have (b_f=-1) and (b_g=-2). Since (-2<-1), the (y) - intercept of (g(x)) is lower than that of (f(x)).

Answer:

The line of (g(x)) is steeper and has a lower (y) - intercept.