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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.

How do I write this and explain this out, math is not really a strong point with me especially when it comes to explaining something like this out?

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Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
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
Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
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:
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.
 So b=-2. Therefore, your line equation in the slope-intercept form looks as follows: