A linear equation in slope-intercept form is given by the following formula:

          y = mx + b  ,    

     where 'm' is the slope of the line and 'b' is the y-intercept of the line (i.e., the point on the graph where the line intersects with the y-axis, or the point on the line where x= 0).

You are given that the line in question passes through the point (0, 1) and has a slope of -9. That is, we are given the following information:

      (x, y) = (0, 1)   ==>   x = 0 ,  y = 1

      slope = m = -9

Using the slope-intercept formula, we plug in these numbers and solve for the y-intercept (b):

          y = mx + b

          1 = (-9)·(0) + b

          1 = 0 + b

          1 = b

We can now state the equation of this line in slope-intercept form using its given slope (m = -9) and its y-intercept (b = 1), which we just solved for:

          y = mx + b

          y = -9x + 1

Since we are gine a point and the slope, start with the point slope form and slove for y to get the slope intercept form

(Y - Y₁) = m (X - X₁)

Y - 1 = -9 (X -0)

Y - 1 = -9X

Y = -9X + 1

This method can be used anytime you have a point and the slope to fine the slope intercept form.

The slope-intercept form of a line is y = mx + b. To write the equation in slope-intercept form we need to find "m" and "b". The "y" and "x" don't change. The m stands for the slope of the line which is the vertical change (change in the y coordinates) divided by the horizontial change (change in the x-coordinates). In this problem they give you m, the slope of the line. They say m = -9 (also = -9/1). This means you can pick any point on the line and go down (negative y direction) 9 units, then from there you can now go 1 unit to the right (positive x direction) and mark a point on the line. If done correctly you should hit the line. Now we need the b, this is the y-coordinate of the point (x,y) where the line crosses the y-axis, called the y-intercept. The problem tells you the point (0,1) is on the line. Since the 1st coordinate (the x-coordinate) is zero this means our point, (0,1), is on the y-axis, so it is the y-intercept. So from the point (0,1) we get b = 1, since x = 0. Now we are ready to write the equation of the line in slope-intercept form. Replace (substitute) the m with -9 and replace b with 1, do not change the y or x.

 So for y = mx + b, with m = -9 and b = 1, we should get y = -9x + 1 and this is our answer.