How do you write the equation of line given x-intercept of 4 and a slope of 3/4?

The equation of a line in #color(blue)"slope-intercept form"# is

#color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))#
where m represents the slope and b, the y-intercept.

Here we have a coordinate point (4 ,0) and #m=3/4#

So the partial equation is #y=3/4x+b# and to find b we substitute x = 4 and y = 0 into the partial equation.

#rArr0=3/cancel(4)xxcancel(4)+b=3+brArrb=-3#

#rArry=3/4x-3" is the equation"#

Let #color(purple)(k)# be some constant such that
#color(white)("XXX")y=color(green)(m)x+color(purple)(k)#
where #color(green)(m)# is the slope.

We are told that #color(green)(m)=color(green)(3/4)#
and
the x-intercept is #color(brown)(4)#

If the x-intercept is #color(brown)(4)#
this means that #x=color(brown)(4)# when #y=color(cyan)0#

So our general equation: #y=color(green)(m)x+color(purple)(k)#
becomes
#color(white)("XXX")color(cyan)(0)=color(green)(3/4)*color(brown)(4)+color(purple)(k)#

#color(white)("XXX")rarr color(purple)(k)=color(blue)(-3)#

and our equation is
#color(white)("XXX")y=color(green)(3/4)xcolor(blue)(-3)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using the above logic we can see that the general case when given
a slope of #color(green)(m)# and
an x-intercept of #color(purple)(k)#
is
#color(white)("XXX")y=color(green)(m)xcolor(blue)(-k/m)#