Answer:
y = -5/3x + 13/3
Explanation:
(-1, 6) and (5, -4).
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-4 - 6) / (5 - (-1))
Simplify the parentheses.
= (-10) / (5 + 1)
= (-10) / (6)
Simplify the fraction.
-10/6
= -5/3
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = -5/3x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (5, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -5/3(5) + b
To find b, multiply the slope and the input of x(5).
-4 = -25/3 + b
Now, add 25/3 to both sides to isolate b.
-4 ⇒ -12/3
-12/3 + 25/3 = 13/3
13/3 = b
Plug this into your standard equation.
y = -5/3x + 13/3
This is your equation.
Check this by plugging in the other point you have not checked yet (-1, 6).
y = -5/3x + 13/3
6 = -5/3(-1) + 13/3
6 = 5/3 + 13/3
6 = 18/3
6 = 6
Your equation is correct.
Hope this helps!