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## What is the slope of a line whose graph is parallel to the graph of -6x+y=4?

Also, what is the slope of a line whose graph is perpendicular to the graph of -6x+y=4?

-6x + y = 4

you can move the variables around to get the form: y = mx + b, which is the slope intercept form.

y = 6x + 4

here: m = 6, b = 4

m is the slope of the line, so slope is 6

any line parallel to this line will also have the slope of 6

any line perpendicular to the given line will have the slope of:  -1/m1

we know m1 = 6, so the perpendicular line will have the slope of:   -1/6

parallel lines have the same slope. so, first, you solve the given equation for y and put it in slope-intercept form, y=mx+b where m is the slope.

-6x+y=4

+6x to both sides

y=6x+4

so the slope is 6

perpendicular lines have opposite reciprocal slopes, so the slope of that line is -1/6

First rearrange the equation of the line given into slope-intercept form, which is given by:

y = mx + b ,   where m is the slope of the line and b is the y-intercept.

So to change the equation of the line given into slope-intercept form, we solve it for y:

-6x + y = 4          add 6x to both sides of the equation

-6x + y + 6x = 4 + 6x

6x - 6x + y = 6x + 4

y = 6x + 4

With this, we find the slope (m) of this line   ==>   slope:     m = 6

Two lines that are parallel to one another have the same slope. So since the slope of the given line is 6, then the slope of the line parallel to it is also 6.

Two lines that are perpendicular to one another have slopes that are opposite reciprocals. So since the given line has a slope of 6, then the slope of the line perpendicular to it is the opposite reciprocal of 6, which is -1/6.