Answer:
[tex]y = \frac{-3}{2}x + 3[/tex]
Step-by-step explanation:
Step 1 - Calculate slope first via the equation:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
Where x1 and y1 are the coordinates of the first set whereas x2 and y2 are the second set. Plug the variables in:
[tex]\frac{6 - (-3)}{-2 - 4} \\\frac{6 + 3 )}{-2 - 4} \\\frac{9}{-6}[/tex]
Which simplifies to:
[tex]\frac{3}{-2}[/tex]
Now, in the line equation form we know x:
y = mx + c
y = [tex]\frac{3}{-2}[/tex]x + c
Step 2 - Calculate y intercept
Plug the variables of one point into the above equation:
y = [tex]\frac{3}{-2}[/tex]x + c
[tex]6 = \frac{3}{-2}(-2) + c[/tex]
[tex]6 = \frac{3}{-2}(-2) + c \\6 = 3 + c\\6 - 3 = c\\c = 3\\[/tex]
Meaning that the full line equation is:
[tex]y = \frac{-3}{2}x + 3[/tex]
Hope this helps!
