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What is the equation of a line with slope 4 and passing through (-1, -6), and how do I write it in slope-intercept form.

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2 Answers

The equation of the line of slope 4 is y=4x+b.  The line goes through (-1,-6) If you step 1 unit positive in the x direction you reach the y-axis, (x=0).  In order to remain on the line you need to go up 4 units, that is from -6 to -2.  y=4x-2
The slope-intercept form looks like this:
 
y=mx+b, where m is the slope, b is the intercept.
 
You are given that the slope is 4, therefore m=4.
 
So you have:
 
y=4x+b;
You need to find b. You also know that the line passes through the point (-1, -6). It means that if you plug in -6 for y and -1 for x, you shall obtain correct equality.
 
That is,
 
-6=4*(-1)+b shall be correct. Or -6=-4+b. Add 4 to both sides to get rid of -4 in the right side.
 
-6+4=-4+4+b.
 
-2=b
 
 So b=-2. Therefore, your line equation in the slope-intercept form looks as follows:
 
y=4x-2