Find the slope of a line perpendicular to the line whose equation is x, plus, 4, y, equals, 28x+4y=28. Fully simplify your answer.
To find the slope of the line, we first need to rewrite the equation in slope-intercept form, which is y = mx + b.
Rearranging the given equation, we have:
28x + 4y = 28
4y = -28x + 28
y = (-28/4)x + 7
y = -7x + 7
Comparing this equation to y = mx + b, we can see that the slope of the given line is -7.
The slope of a line perpendicular to this line will be the negative reciprocal of -7.
The negative reciprocal of -7 is:
-1/(-7) = 1/7
So, the slope of a line perpendicular to the line 28x + 4y = 28 is 1/7.