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what is the equation in slope-intercept form of the line that passes through (-1,2) and has a slope of 4?

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2 Answers

Another method to try is point-slope form
 
y-y1= m (x - x1)
 
(x1, y1) is your point and m is your slope. 
 
So input the information you are given into the formula above. 
 
y-(2)= 4(x-(-1))
 
Then you simplify. 
 
y-2= 4(x+1)
 
y-2 = 4x+4
 
And then you solve for y. (In other words, put the equation into slope-intercept form, y=mx+b. Your slope is m and your intercept is b)
 
y = 4x + 6
 
From this we can see that our slope is 4, and our y-intercept is (0,6). 
 
CHECKING:
 
Remember to always check your answer: 
 
To check we take our final answer: 
 
y = 4x + 6
 
and input our original point, (-1, 2)
 
2 = 4(-1) + 6
 
2 = (-4) + 6
 
2 = 2
 
So our answer checks! 
 
 
 
Remember y= mx+b. I don't know any quicker thing to tell you to help you remember.
 
Just practice it over and over and over, day after day, reminding yourself:
 
m is the slope, has this formula m=(y2-y1)/(x2-x1), the change in y divided by the change in x.
b is the intercept, where the line crosses the y-axis.  If the x value is 0, than the slope is gone and y=b.
 
So you have a line, y=mx+b.  You know that a point on that line is at (-1,2). 
If you put that value of that point into the form, you would have:
 
2=m(-1)+b.  so there are two variables you don't know about the line which goes through this point:
the slope of the line and the point where it crosses the y-axis.  If you know those to variables, you would be able to predict all other points on the line.
 
Where there are two variables, you can not solve an equation.  But you know one of the variables for this line: the slope is 4.
 
2=(4)(-1)+b.  You can multiple 4 by -1, get -4.  This means that 2=-4+b.  Solve for b and you know that the line which goes through that point and has a slope of 4 fills out the slope-intercept form like:
 
y=4x+___.