Sue and kathy were doing their algebra homework. they were asked to write the equation of
the line that passes through the points (-3,4) and (6,1). sue wrote y - 4 = -(x + 3) and kathy
wrote y = -x + 3. justify why both students are correct.

both students are incorrect

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

Slope = (y2 - y1)/(x2 - x1)

y2 = 1

y1 = 4

x2 = 6

x1 = - 3

Slope = (1 - 4)/(6 - -3) = -3/9 = -1/3

To determine the intercept, we would substitute m = -1/3, x = 6 and y = 1 into y = mx + c. It becomes

1 = -1/3 × 6 + c = -2 + c

c = 1 + 2 = 3

The equation becomes

y = -x/3 + 3

If the equation was written in the slope intercept form which is expressed as

y - y1 = m(x - x1)

It becomes

y - 4 = -1/3(x - - 3)

y - 4 = -1/3(x + 3)

Both students are incorrect