Find the equation of the straight line that passes through the points (1, 8) and (5, 0). Give your answer in the form of ‘ = + ’. tysm

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asked Jun 28, 2024 159k views

1 Answer

Djole · Answer 1 · 2024-07-02T14:59:36+0000

Certainly! Here's the solution to find the equation of the straight line that passes through the points (1, 8) and (5, 0):

We can use the formula for the equation of a straight line, which is:

$\sf y - y_1 = m(x - x_1) \\$

where
$\sf (x_1, y_1) \\$ represents one of the points on the line and
$\sf m \\$ is the slope of the line.

First, let's find the slope
$\sf m \\$ :

$\sf m = (y_2 - y_1)/(x_2 - x_1) \\$

Substituting the coordinates of the given points into the formula, we have:

$\sf m = (0 - 8)/(5 - 1) \\$

$\sf m = (-8)/(4) \\$

$\sf m = -2 \\$

Now that we have the slope, let's choose one of the points (1, 8) and substitute it into the equation:

$\sf y - 8 = -2(x - 1) \\$

Expanding and rearranging the equation, we get:

$\sf y - 8 = -2x + 2 \\$

Now, let's simplify it further:

$\sf y = -2x + 2 + 8 \\$

$\sf y = -2x + 10 \\$

Therefore, the equation of the straight line that passes through the points (1, 8) and (5, 0) is:

$\sf y = -2x + 10 \\$

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