equation is y = 8x - 2
standard form of a linear equation is ax + by = c
slope intercept form of a linear equation is y = mx + b
point slope form of a linear equation is y - y1 = m(x - x1)
m is the slope
b is the y intercept
your equation is y = 8x -2
this is in the slope intercept form of a linear equation of y = mx + b
m = 8
b = -2
the slope of your equation is 8
the y intercept of your equation is -2
the graph of your equation looks like this:
i drew a horizontal line at y = -2 so you can see that the equation crosses the y-axis at y = -2.
if you plot the values of y from the values of x from x = -3 to x = +3, you would get a table that looks like this:
x y = 8x-2 change in x change in y
-3 -26 - -
-2 -18 1 8
-1 -10 1 8
0 -2 1 8
1 6 1 8
2 14 1 8
3 22 1 8
the table shows that when x = 0, y = -2.
this means the y intercept is equal to -2.
the change in x column is the difference between the value of x in each row and the value of x in the row above it.
the change in y column is the difference between the value of y in each row and the value of y in the row above it.
you can see that when x change by a value of 1, the corresponding value of y changes by a value of 8.
that's your slope of 8 which is equal to the change in y divided by the change in x.