Question

Write the equation of the line in fully simplified slope-intercept form.
(6,-10) and (-6,0)

Answer 1

To find the slope, we can use the formula:

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

where (x1, y1) = (6, -10) and (x2, y2) = (-6, 0).

So, m = (0 - (-10))/(-6 - 6)

= 10/-12

= -5/6.

Let's call the slope m = -5/6 and use the point-slope form of the equation of a line:

y - y1 = m(x - x1).

Substituting the values (x1, y1) = (6, -10):

y - (-10) = (-5/6)(x - 6).

This simplifies to:

y + 10 = (-5/6)(x - 6).

Multiplying through by 6 to clear the fraction:

6(y + 10) = -5(x - 6).

Simplifying:

6y + 60 = -5x + 30.

Rearranging the terms:

6y = -5x - 30.

Finally, we can write the equation in fully simplified slope-intercept form:

y = (-5/6)x - 5.