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Question

what is the slope of the line that passes through (-4,7) and (-6, -4)

Answer 1

Stephenson provided a great response here, but I thought I might add another way to look at this problem. The question is looking for the slope between two points, in affect the angle of the line between the points. Therefore, as long as the angle doesn't change we can translate our two points around, as long as we move them together the angle will be the same. Think of this as sliding the two points around on the graph. The advantage here is that we can make one of the points the origin.

Lets take the point (-6,-4)

To make this point the origin we need to add 6 to the x value and 4 to the y value

So lets add (6,4) to both points. Then we get the two points

(-6+6,-4+4) and (-4+6,7+4)

(0,0) and (2,11)

from here we can use the slope formula

(x₁, y₁) and (x₂, y₂), is: m = (y₂ - y₁) / (x₂ - x₁)

and we get the same answer m = (11-0)/(2-0) = 11/2

This translation adds an extra step, but can help check your answers as it give some intuition since we are starting from 0,0

Answer 2

Formula for slope of a line between two points, (x₁, y₁) and (x₂, y₂), is:

m = (y₂ - y₁) / (x₂ - x₁)

We are given two points: (-4, 7) and (-6, -4), so:

m = (-4 - 7) / (-6 - -4)

m = -11 / -2

m = 11/2

Hope this was helpful.