Question 21495
Hello There:

There are many different forms for writing the equation of a line.  For this problem, we need to know two of them:

y = m*x + b

This is the "slope-intercept" form where m is the slope and b is the y-intercept.  They call it the slope-intercept form because you can see at a glance what the slope and y-intercept are when looking at the equation.

For example, y = -7*x + 13

We can see that this line has a slope of -7 and crosses the y-axis at (0,13).

The other form that we need to know is the "point-slope" form.  We use this form when we know the slope of the line and the coordinates of one point on the line.

This is the information that you've been given.  The slope is -2, and the known point is (-3, -5).

If the known point is (a, b), and the slope is m, then the point-slope form is:

y - b = m*(x - a)

So, substituting the known coordinates for a and b, and the slope, we get:

y - (-5) = (-2)*(x - [-3])

y + 5 = -2*(x + 3)

y + 5 = -2*x - 6

y = -2*x - 6 - 5

y = -2*x - 11

So, as you see, by solving the point-slope form for y, we get the slope-intercept equation of the line.

This line has a slope of -2, and it crosses the y-axis at (0, -11).

~ Mark