A line has the equation y = 5x + 4.(a) This line has slope of ___________?
(b) Any line parallel to this line has slope _________?
(c) Any line perpendicular to this line has slope _______?
5
5
-1/5
To find the answers to these questions, we can analyze the equation of the given line, which is in slope-intercept form (y = mx + b), where m represents the slope.
(a) In the equation y = 5x + 4, the coefficient of x is 5. Therefore, the slope of this line is 5.
(b) Any line that is parallel to the given line will have the same slope. So, the slope of any line parallel to y = 5x + 4 is also 5.
(c) The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line. In this case, the slope of the original line is 5. Thus, the slope of any line perpendicular to y = 5x + 4 would be -1/5.