What is the equation of the line that passes through the point left bracket, 6, comma, minus, 8, right bracket(6,−8) and has a slope of minus, start fraction, 2, divided by, 3, end fraction−

Question

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Answer 1

To find the equation of a line, we use the point-slope form, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Given that the point is (6, -8) and the slope is -2/3, we can substitute these values into the equation:

y - (-8) = (-2/3)(x - 6)

Simplifying:

y + 8 = (-2/3)(x - 6)

Multiplying (-2/3) by (x - 6) gives:

y + 8 = (-2/3)x + 4

Subtracting 8 from both sides:

y = (-2/3)x - 4 - 8

Simplifying:

y = (-2/3)x - 12

So, the equation of the line that passes through the point (6, -8) with a slope of -2/3 is y = (-2/3)x - 12.

Answer 2

try again

Answer 3

Apologies for the confusion. Let's solve it again.

We are given that the line passes through the point (6, -8) and has a slope of -3/2.

Using the point-slope formula, the equation of the line is:

y - y1 = m(x - x1)

Substituting the values, we have:

y - (-8) = (-3/2)(x - 6)

Simplifying:

y + 8 = (-3/2)(x - 6)

Multiplying (-3/2) by (x - 6) gives:

y + 8 = (-3/2)x + 9

Subtracting 8 from both sides:

y = (-3/2)x + 1

So, the equation of the line that passes through the point (6, -8) with a slope of -3/2 is y = (-3/2)x + 1.