Final answer:
The slope of a line perpendicular to another line with a slope of 5 is – 1/5. This result comes from the fact that perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
The slope of a line that is perpendicular to the line represented by the equation y – 5x = 5 can be found by first putting the equation into slope-intercept form to determine its slope. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. For the given equation, adding 5x to both sides gives us y = 5x + 5. Therefore, the slope of the original line is 5. The slope of a line perpendicular to another line is the negative reciprocal of the original line’s slope. Hence, the slope of the perpendicular line is – 1/5. This illustrates how the m term in an equation for a straight line determines the shape of the line.
Remember that a positive slope indicates that the line moves up as x increases, while a negative slope indicates that the line moves down as x increases. The steeper the slope, the steeper the line. In the case of lines that are perpendicular, their slopes have an inverse relationship.