X AND Y INTERCEPT

OK....we'll answer BOTH of your posted questions

Equation of a line  :  y = mx + b    m = slope   b= y axis intercept

slope is rise/ run    ....for the two popints you have listed =  (4-(-8))/ (6-(-3))  =   12/9

y= 12/9 x + b     substitute one of your points

4= 12/9 (6) + b

4 = 72/9 + b

4 = 8 + b          b= -4

y= 12/9x -4    is the equation for your line    the y intercept is where x= 0       -4

the x-intercept is where y= 0       0 = 12/9x -4      x= 4 (9/12) = 3     

(6,4) and (-3,-8)

Let's get the slope between these two points and then write an equation of the line through them....

slope = m  =    [ -8 -4] /  [-3 - 6]   =  -12/-9  =  4/3

Using one of the points, we can write the equation of the line as follows :

y - y1   = m ( x - x1)      

where   (x1, y1)  =  (6,4)       [we could have used the other point, as well ].....so we have

y - 4 = (4/3)(x - 6)

y - 4  = (4/3)x - 8    add 4 to both sides

y = (4/3)x - 4

To find the y intercept, let x = 0   ......

y = (4/3)(0)  - 4     =  -4 ........so the y intercept is (0, -4)

To find the x intercept, let y = 0

0 = (4/3)x  - 4       add 4 to bot sides

4 = (4/3)x          multiply both sides by 3/4

3  = x       so.....the x intercept  is    (3, 0)

Here's the graph :  https://www.desmos.com/calculator/iabghxul4f