Hey there! I'm happy to help!
SLOPE
To find the slope, you divide the difference of the y values by the difference in the x values.
10-(-2)=10+2=12
-6-(-3)=-6+3=-3
12/-3=-4
So, our slope is -4.
Y- INTERCEPT
To find the y-intercept, we plug our slope and one of our points into the slope intercept equation (y=mx+b) and solve for b, which is the y-intercept. We will use the point (-6,10).
10=-4(-6)+b
Flip the equation so b is on the left.
-4(-6)+b=10
24+b=10
Subtract 24 from both sides.
b=-14
Our y-intercept is -14.
EQUATION
The slope intercept equation is y=mx+b, where m is the slope and b is the y-intercept. Therefore, we have the following answers.
Slope: -4
y-Intercept: -14
Equation of the Line: y=-4x-14
Have a wonderful day! :D