If y=x-6 were change to y=x-8 how would the graph of the new function compare with the first one ?

Answer: -  The lines of both functions have the same slope. - The line of the first function intercepts the y-axis at the point (0,-6) and the  line of the new function intercepts the y-axis at the point (0,-8). - The new graph is the graph of the first function but shifted 2 units down.Step-by-step explanation: The equation of the line in slope-intercept form is: [tex]y=mx+b[/tex] Where the slope is "m" and the intersection of the line with the y-axis is "b". Given the function in the form [tex]y=x-6[/tex], you can identify that: [tex]m=1\\b=-6[/tex] And from the new function in the form  [tex]y=x-8[/tex], you can identify that: [tex]m=1\\b=-8[/tex] This means that the lines of both functions have the same slope, but the line of the first function  [tex]y=x-6[/tex] intercepts the y-axis at the point (0,-6) and the  line of the new function  [tex]y=x-8[/tex] intercepts the y-axis at the point (0,-8). Therefore, the graph of the new function is 2 units below of the function [tex]y=x-6[/tex], or, in other words, the new graph is the graph of the first function but shifted 2 units down.