Which equation represents a line with a slope of negitive 2/3that passes through point (5, - 2)

Answer 1

So when given a slope, and one point on that line, we can find an equation in slope-intercept form (y=mx+b):

1) write out the slope-intercept form:

y=mx+b

In slope intercept form, 'm' represents the slope, 'b' represents the y-intercept, and the x & y represent the x-value (x-coordinate) and a y-value (y coordinate) of an ordered pair.

We do not know the b (y-intercept), but we do have an m(slope) and an ordered pair (an x-value and y-value). All we need to do now is plug in the values we were given.

Our slope is -2/3, so m = -2/3 and our point given is (5,-2), so x=5 and y=-2

2) Plug in given information into slope intercept form:

y = mx+b

-2 = (-2/3)(5)+b Notice how we now have enough information to isolate the b (get b all by itself), solving for b:

3) Solve for b:

-2 = (-2/3) (5) + b

-2 = (-10/3) + b multiplied -2/3 and 5 together

-2+ (10/3) = (-10/3) + (10/3) + b Added 10/3 to both sides

(Whatever you do to once side, you HAVE to do to the other side.)

4/3= 0 + b The negative 10/3 and positive 10/3 cancel each other out on the right side, leaving 0, which we can remove completely.

4/3=b; We now have found our b (y-intercept).

Therefore, since we know the slope (m) is -2/3 and the y-intercept (b) is 4/3, we now have enough information to write this equation in slope intercept form:

4) write out the slope intercept form with the m we were given and the b we found:

Our answer is y = (-2/3)x+(4/3)

And we're done!