You have the following equation:
8.9x-5.3y-9.1 = 0 (1)
The general form of a line equation is given by:
y = mx + b (2)
where m is the slope and b is the y-intercep of the line.
In order to find the x-intercept and y-intercept, you first write the equation (1) in the same form of the equation (2). Then, you solve for y in the equation (1), just as follow:
8.9x-5.3y-9.1 = 0
-5.3y = -8.9x + 9.1
y = (-8.9x + 9.1)/(-5.3) = 1.67x - 1.71
Then, the line equation is:
y = 1.67x - 1.71
If you compare the previous equation with the equation (2) you have that b=-1.71
y-intercept = -1.71
To obtain the x-intercept, you make y=0 and solve the for x, as follow:
0 = 1.67x - 1.71
1.67x = 1.71
x = 1.71/1.67 = 1.02
Then, the x-intercept is x = 1.02