y=-2/3x+5 that goes through the point (6,0)

Answer 1

To check if the line y = -2/3x +5 goes through the point (6,0) , we can substitute x = 6 and y = 0 into the equation and see if the equation holds true.

The given equation is :

y = -2/3x+5

Substitute x = 6 and y = 0 :

0 = -2/3(6) + 5

Now calculate :

0 = -(2 x 6 /3) + 5

0 = -4 + 5

0 = 1

Since 0 ≠ 1 the point (6,0) does not lie on the line y = -2/3x + 5.

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Answer 2

Assuming that you are asking for a line that is parallel to y = -2/3 x + 5 that goes through the point (6,0)

You are already given the same slope (m = -2/3), and a point. All that is left is to find the y-intercept (b) by plugging in the given point.

slope -intercept form:

y = mx + b

plug in slope (m) and point (x,y)

0 = (-2/3)(6) + b

simplify

0 = -12/3 + b

0 = -4 + b

b = 4

Now you have the equation of the line that is parallel and goes through the point given

Answer: y = -2/3x + 4

IF you wanted a line that is PERPENDICULAR to the given line and goes through the given point.

You must flip the sign and the fraction of the slope you are given.

Given:

m = -2/3

NEW PERPENDICULAR SLOPE:

m = +3/2

(notice the flipped sign AND fraction)

Now you complete the same steps as above. Plug in the new slope and the new point to find the y-intercept.

slope-intercept form:

y = mx + b

plug in slope (m) and point (x,y)

0 = (3/2)(6) + b

Simplify

0 = 18/2 + b

0 = 9 + b

b = -9

Now you have the equation of the line that is PERPENDICULAR and goes through the point given.

Answer:

y = +3/2x - 9

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