You have the following equation:
3x + 4y = 8
In order to determine the slope, y-intercept and x-intercept, you consider that the general form of the equation of a line is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept
You solve the equation 3x + 4y = 8 for y, as follow:
3x + 4y = 8 subtract 3x both sides
4y = -3x + 8 divide both sides by 4
y = -3/4 x + 2
By comparing the previous eqaution with the general form y = mx + b, you have:
slope = -3/4
y-intercept = 2
Now, to find the x-intercpet of the equation, you equal y to zero and solve for x, just as follow:
y = -3/4 x + 2 replace y = 0
0 = -3/4 x + 2 subtrac 2 both sides
-2 = -3/4 x multiply by -4/3 both sides
2(4/3) = x
8/3 = x
Hence, you have:
x-intercept = 8/3
x-intercpets are the same that zeros of the equation.