Consider the following equations: f(x) = 2x – 2 and g(x) = 5 - xa. The two equations represent lines on a graph, describe the difference in slope and y-intercept.
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Answer:The difference in slopes of [tex]f(x)\ and\ g(x)[/tex] is = 3We can say slope of [tex]f(x)[/tex] is positive and 3 more than slope of [tex]g(x)[/tex] while slope of [tex]g(x)[/tex] is negative.Difference of y-intercepts of [tex]f(x)\ and\ g(x)[/tex] is = -7We can say the y-intercept of [tex]g(x)[/tex] is positive and 7 units above [tex]f(x)[/tex] while y-intercept of [tex]f(x)[/tex] is negative.Step-by-step explanation:Given equation:[tex]f(x) =2x - 2[/tex][tex]g(x) =5-x[/tex]We need to find the difference of slopes and y-intercepts of the given equations.The standard form of a slope intercept equation of line is given by:[tex]y=mx+b[/tex]where [tex]m[/tex] represents slope and [tex]b[/tex] represents y-intercept of line.Writing the given equations in standard form to find slope and y-intercept.[tex]f(x) =2x +(-2)[/tex]Slope = 2 and y-intercept =-2[tex]g(x) =(-1)x+5[/tex]Slope = -1 and y-intercept =5The difference in slopes of [tex]f(x)\ and\ g(x)[/tex] is = [tex]2-(-1)=2+1=3[/tex]We can say slope of [tex]f(x)[/tex] is positive and 3 more than slope of [tex]g(x)[/tex] while slope of [tex]g(x)[/tex] is negative.Difference of y-intercepts of [tex]f(x)\ and\ g(x)[/tex] is = [tex]-2-5=-7[/tex]We can say the y-intercept of [tex]g(x)[/tex] is positive and 7 units above [tex]f(x)[/tex] while y-intercept of [tex]f(x)[/tex] is negative.