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Question 98305: A line having an x-intersept of 4 and passing through the point(-2, -6).
Answer by missjambajuice(1)   (Show Source):
You can put this solution on YOUR website! When the question asks for a line, it's asking for the equation of the line.
It says that the line has an x-intercept of 4. That means that the line intercepts or touches the x-axis at (4,0). The question also says that the line passes through point (-2,-6). If you find 2 points on the line, you can find the equation of the line. Two points (4,0) and (-2,-6). Basic line equation: y=mx+b
The x and y represents points on the line. m represents the slope of the line. slope is (y2-y1)/(x2-x1). (note that (x1,y1) and (x2,y2) are points on the line; it's not x*2, it's x number 2, it's not y*1, its y number 1). b represents the y-intercept which is the point on the y-axis where the line intercepts.
To find the equation of the line:
1. find the slope, which is m in y=mx+b
two points (4 ,0 ) and (-2,-6) = (x1,y1) and (x2,y2)
slope=m=(y2-y1)/(x2-x1)
=(-6- 0)/(-2- 4)
=(-6)/(-6)
= 1
so far we have found part of the equation: y=1x+b
2. find b, which is the y-intercept in y=1x+b
y-intecept is the point on the y-axis where the line intercepts or touches.
to find b, substitute in an (x,y) point on the line in y=1x+b
point (4,0) is on the line
y=1(x)+b
0=1(4)+b
0=4 +b
-4=b
This means that the y-intercept is at -4
Since we have found m and b, we can compute the equation of the line
basic line equation: y=mx+b
we found m and b, m=1, b=-4
y=1x+(-4)
y=x-4 <=== That is the equation of the line!
Conclusion: to find line, find two points, slope(m), and y-intercept(b)
also MEMORIZE basic line equation: y=mx+b
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