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Write the equation of the line that passes through (7,−7) and (3,8).

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Final answer:

The equation of the line that passes through (7, -7) and (3, 8) is found by first calculating the slope (m) which is -15/4, and then using the point-slope form to arrive at the line's equation, which is y = (-15/4)x + 77/4.

Step-by-step explanation:

To write the equation of the line that passes through the points (7, -7) and (3, 8), you first need to find the slope (m) of the line. The slope is calculated by the change in y divided by the change in x:

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

Substitute the points into the formula:

m = (8 - (-7)) / (3 - 7)

m = 15 / -4

So the slope m is -15/4.

Now use point-slope form to write the equation of the line:

y - y1 = m(x - x1)

Using point (7, -7):

y - (-7) = (-15/4)(x - 7)

Simplify the equation:

y + 7 = (-15/4)x + (15/4)*7

y = (-15/4)x + 105/4 - 28/4

y = (-15/4)x + 77/4

Therefore, the equation of the line is y = (-15/4)x + 77/4.

User WB Lee
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