Mathematics: Determine the slope and y-intercept of a line that passes through the points (-2, 6) and (4, -3).

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Determine the slope and y-intercept of a line

gerkera88

04.11.2021

$y = \frac{-3}{2}x + 3$

Step-by-step explanation:

Step 1 - Calculate slope first via the equation:

$\frac{y2 - y1}{x2 - x1}$

Where x1 and y1 are the coordinates of the first set whereas x2 and y2 are the second set. Plug the variables in:

$\frac{6 - (-3)}{-2 - 4} \\\frac{6 + 3 )}{-2 - 4} \\\frac{9}{-6}$

Which simplifies to:

$\frac{3}{-2}$

Now, in the line equation form we know x:

y = mx + c

y = $\frac{3}{-2}$ x + c

Step 2 - Calculate y intercept

Plug the variables of one point into the above equation:

y = $\frac{3}{-2}$ x + c

$6 = \frac{3}{-2}(-2) + c$

$6 = \frac{3}{-2}(-2) + c \\6 = 3 + c\\6 - 3 = c\\c = 3\\$

Meaning that the full line equation is:

$y = \frac{-3}{2}x + 3$

Hope this helps!

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