Equation of a line, use the slope intercept formula for points (3,-6) and (5,8) including a check. please help me learn instead of telling me the answer :)

i’ll show u what i have so far

y=7x-27

Step-by-step explanation:

The equation of a line is given by y=mx+C where m is the gradient of the line or slope and c is the intercept on your axis. according to your question, you are given two point on (3,-6) and (5,8). so we can get the gradient m= Y2-Y1/X2-X1= gradient. so Y1= -6, Y2=8 , X1=3, X2=5

slope= 8-(-6)/5-3=14/2=7. so m=7so the equation of line can be written in form y=7x+C. but we need to find C. C can be gotten from where the line passes through (3,-6) that is when x=3, y=-6. so we can find C from that point. -6=7(3)+C..so we have -6=21+C. C=-6-21=-27

so the equation of the line is y=7x-27