Find the expression for the line segment joining these two points.?

Question

(-2,1) and (4,-6)

Answer 1

the slope (or gradient) is m=(-6-1)/(4+2)=-7/6

y-1=(7/6)(x+2), which is in point-slope form

Answer 2

I kind of like the parametric form: p = p1 + t (p2 - p1)

Where p1 is the first point, p2 is the second point, p is any point on the line, and t is the parameter that goes from 0 to 1 for the line segment, or -infinity to +infinity for the entire line.  To compute the value for x or y, you set up a similar equation for each one:

x = x1 + t (x2 - x1)

y = y1 + t (y2 - y1)

If you solve both of the above for t and set them equal to each other, you'll get a non-parameterized form of a line equation.  You can then solve that for x or y.

Answer 3

Hi,

Slope = m = change in y values/change in x values = (-6-1)/(4-(-2)) = -7/6

Now the equation of line is:

y - y1 = m(x - x1)

=> y - 1 = (-7/6)(x - (-2))

=> y - 1 = -7x/6 -7/3

=> y = 1 -7x/6 -7/3

=> y = -7x/6 - 4/3

So the equation of the line is:

y = -7x/6 - 4/3

slope = m = -7/6

y-intercept = c = -4/3

hope this helps. keep smiling. bye.