the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8. what is the value of w

Use the point-slope formula for the eqn of a str line:

y-k = m(x-h), where (h,k) is any point on the line.

Suppose we first focus on the given point (-10,4). Let (h,k) = (-10,4).

Then y-k = m(x-h) becomes y-4 = m(x-[-10])

The other point is (-6,w), where w is the unknown we must determine.

w-4 = (1/8)(-6+10). Find w:

Mult both sides by 8 to remove the fraction 1/8:

8w-32 = -6 + 10 = 4. Then 8w = 32+4 = 36. w = 36/8 = 4.5, or 9/2 (ans.)

lisboa lisboa · Answer 2 · 2021-10-01T14:40:58+02:00

The value of 'w' using the given slope is [tex]\frac{9}{2}[/tex]

Given :

the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8

apply slope formula

[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values given in the points and make it equal to 1/8

[tex]slope =\frac{4-w}{-10+6}=\frac{1}{8} \\\frac{4-w}{-4}=\frac{1}{8}\\(4-w)(8)=-4(1)\\32-8w=-4\\-8w=-4-32\\-8=-36[/tex]

Divide both sides by -8

[tex]w=\frac{-36}{-8} =\frac{9}{2}[/tex]

The value of 'w' is [tex]\frac{9}{2}[/tex]

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