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Question 1083356: Could you please tell me the answer to this question: What is the equation of a line that passes through the points (0,3) and (-2,-3)? I know the equation for a line is (y=mx + b) but I'm unsure on how to do it. Thank you very much :D
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the line passes through the points (0,3) and (-2,-3)
those points are in (x,y) format.
the slope of a straight line is (y2-y1)/(x2-x1)
assign one of the points to (x1,y1) and assign the other point to (x2,y2)
i chose (x1,y1) = (0,3) and (x2,y2) = (-2,-3).
you could have chosen it the other way around ((x1,y1) = (-2,-3) and (x2,y2) = (0,3)).
you'll get the same slope either way.
the slope intercept form of the line is y = mx + b
m is the slope
b is the y-intercept.
the formula for the slope, given 2 points is (y2-y1)/(x2-x1)
replace (x1,y1) and (x2,y2) with their respective values, and the formula becomes:
when = (x1,y1) = (0,3) and (x2,y2) = (-2,-3), the slope formula becomes:
slope = (-3-3) / (-2-0) which becomes -6/-2 which becomes 3.
the slope is equal to 3.
since m is the slope, replace m with 3 in the equation of y = mx + b to get y = 3x + b
now all that is left is to find the y-intercept.
replace x and y with the value of one of the points.
either one will do.
i chose (x2,y2) = (-2,-3)
y = 3x + b becomes -3 = 3*-2 + b
this becomes -3 = -6 + b
add 6 to both sides of this equation to get 3 = b
the equation of y = 3x + b becomes y = 3x + 3
the slope is 3 and the y-intercept is 3.
here's a graph of the equation.
you can see that the point (-2,-3) is on the line and the point (0,3) is also on the line.
here's a reference you might find helpful.
http://www.purplemath.com/modules/strtlneq.htm
some tutorials tell you to use the point slope form of the equation to find the y-intercept.
since we already found the slope, our equation is y = 3x + b
to find the y-intercept, use the slope intercept form of the equation of a straight line.
that form is y-y1 = m * (x-x1)
x1 and y1 are any one of the two points you were given.
we'll use (0,3)
the equation becomes y - 3 = 3 * (x-0)
simplify to get y - 3 = 3x
add 3 to both sides to get y = 3x + 3
3 is the y-intercept.
a reference on point slope form of the equation of a straight line can be found here.
http://www.purplemath.com/modules/strtlneq2.htm
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