Question

Write the equation of a line that includes the point (-4,0) and has a slope of -3/5 in slope intercept form

Answer 1

In "slope-intercept form"
  y = mx +b
the value "m" is called the slope, and the value "b" is called the intercept.

There is another form for the equation of a line, called "point-slope form".
  y = m(x -h) +k
where m is still the slope and (h, k) correspond to the (x, y) of the point.

If you write the equation of your line in this "point-slope form", it is easily manipulated to be in the "slope-intercept form".
Fill in
  m = (-3/5)
  h = -4
  k = 0
y = (-3/5)(x -(-4)) +0

Now, you simplify this by using the distributive property.
  y = (-3/5)x -(3/5)*4
  y = (-3/5)x -12/5 . . . . . . . . . the desired equation

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Your understanding of math improves immensely when you become familiar with the terminology. A lot of the rest of it is pattern matching--identifying the parts of one expression that correspond to the parts of another one.

(You will see another version of the "point-slope form", but I find this one the easiest to use for manipulating the equation to other forms.)