How do you write an equation of a line given y-intercept -8 and slope 3?

Consider the standard form of the equation for a strait line:

#y=mx+c#........................................(1)

Where
#m-># is the gradient (slope)
#c->color(white)(.)# is a constant (its value does not change)
#x->color(white)(.)# is a variable (can take on any value you chose)
#y->color(white)(.)# is the dependant variable (the answer)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The gradient (slope)")#
#color(green)("We are told that the gradient (slope) is 3.")#

so equation (1) becomes:

#color(blue)(y=color(green)(3)x+c)#

#color(red)("This is what the graph would look like if there was no "c)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of "color(green)(c))#

Suppose we put the value of the y-intercept (given as -8) into the equation were #c# is. So equation (1) becomes

#color(blue)(y=3xcolor(green)(-8))#

#color(red)("This time the graph look like:")#

So for the equation of a strait line the #c# in the equation is the y-intercept.

Change the value of c moves the plotted line up or down

Imagine for a moment that #c= 2# then the line would cross the y-axis at y=2.

If #c=-3# then the y-intercept would be -3