Question

Find the point-slope equation for the line that passes through the points (5,19) and (-5,-1).

Answer 1

The equation for the slope of a line defined by 2 points, (X1, Y1) and (X2, Y2) is:

(Y2-Y1)/(X2-X1) = (-1-19)/(-5-5) = -20/-10 = 2

The equation of a line is y = mx + b where m is the slope of the line and b is the y-intercept. We know the slope is 2 so we can re-write the equation as:

Y = 2x + b and we can solve for the y-intercept, which is the point where the line crosses the y axis, by putting the xy coordinates from either point (5, 19) or (-5, -1) into the equation:

19 = (2)(5) + b if we use first coordinates

or

-1 = (2)(-5) + b if we use 2nd coordinates

B = 9 in both cases so now our y = mx+b equation becomes:

Y=2x + 9

You can check this by putting in a single x or y coordinate and the equation will yield the other pair of that coordinate.

Answer 2

Answer: y - 19 = 2(x - 5)

Explanation:

The point slope form is expressed as

y - y1 = m(x - x1)

Where

m represents slope

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The given points are (5,19) and (-5,-1)

y2 = - 1

y1 = 19

x2 = - 5

x1 = 5

Slope,m = (- 1 - 19)/(- 5 - 5) = - 20/- 10 = 2

To determine the equation, we would substitute x1 = 5, y1 = 19 and m= 2 into the point slope form equation. It becomes

y - 19 = 2(x - 5)