1. The first step to answering this question is to find the gradient of the line on which the given points are situated. The formula for the gradient is given by:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line
Thus, given that we have the two points (-1, 8) and (5, -2), we can substitute these into the equation above to find the gradient:
m = (-2 - 8) / (5 - (-1))
m = -10 / (5 + 1)
m = -10/6
m = -5/3
2. The second step is to find the equation of the line itself. This can be achieved by substituting the gradient and one point into the formula for a straight line below:
y - y1 = m(x - x1), where m is the gradient and (x1, y1) is one point on the line
We can use either of the given points so let's use (-1, 8), and the gradient of -5/3 that we found in step 1:
y - 8 = (-5/3)(x - (-1))
y = (-5/3)(x + 1) + 8 (Add 8 to both sides)
y = (-5/3)x - 5/3 + 8 (Expand (-5/3)(x + 1) )
y = (-5/3)x + 19/3
Thus, the equation that we are looking for is y = (-5/3)x + 19/3
