write the equation of the line passing through each of the given pairs of points. write yourresults in slope-interceptformwhere possible. (-1, 3) and (4, -2)
get your slope
I got m =(-2-3)/(4+1) = -1
pick one of the points and m=-1 to sub into
y = mx + b, solve for b and rewrite it as
y = -x ......
y=-x + b
y = -x i GET THIS FAR AND I'M LOST.
ok, so we know m=-1 and let's use the point (-1,3)
then in m = mx+b
3 = -1(-1) + b
3 = 1 + b
3-1 = b
then b=2
your equation therefore is y = -x + 2
test it by putting the other point (4,-2)in it
y = -x + 2
Left side= -2
Right side = -(4) + 2
= -2
it works, so we have the correct equation
Reiny, how did you come up with m= (-2-3)/ (4 + 1 = -1
To find the slope (m) of a line passing through two points, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In your case, the given points are (-1, 3) and (4, -2). Let's label them as follows:
Point 1: (x1, y1) = (-1, 3)
Point 2: (x2, y2) = (4, -2)
Now substitute these values into the slope formula:
m = (-2 - 3) / (4 - (-1))
= (-2 - 3) / (4 + 1)
= (-5) / (5)
= -1
So, the slope of the line passing through these two points is -1.
After finding the slope, you can use the point-slope form of a line, y - y1 = m(x - x1), to find the equation of the line.
Using the point (x1, y1) = (-1, 3) and the slope (m) = -1, we can substitute these values into the equation:
y - 3 = -1(x - (-1))
Now simplify:
y - 3 = -1(x + 1)
y - 3 = -x - 1
y = -x - 1 + 3
y = -x + 2
So, the equation of the line passing through the points (-1, 3) and (4, -2) is y = -x + 2 in slope-intercept form.