Quick Answer
Slope = 4/3
y intercept = - 10.7
Comment: Important
When the line is written in the form that is, both the slope and the y intercept can just be read.
But before that let's clarify what we mean. First of all, y = 4x/3 - 10.7 must be what the question says.
It can also be written as y = (4/3)x - 10.7 which is probably the best way.
Some people write it as y = 4/3 x - 10.7 with a space
Since you have written it as y = 4/3 x - 10.7 there is room to believe that you meant y = 4 / (3x) - 10.7. I am however going to interpret it as y = (4x)/3 - 10.7. If that is incorrect, leave me a note and I will correct it. y = 4/(3x) has no consistent slope.
Solution
In this form, the slope and y intercept are both just read from the given equation.
Slope
Whatever coefficient is on the left side of x is the slope. In this case it is just (4/3) The x is not part of the slope. The x and y values must be on opposite sides of the equal sign and the coefficient of y must be 1.
y intercept
That too is just read. If it is on the same side of the equal sign as the x and the slope then it is the value of y when x = 0. So in this case y = (4/3)*0 - 10.7 is y = - 10.7
Slope = (4/3);
y intercept = -10.7
Comment
I have left you a graph to show you the difference
y = 4x/3 - 10.7 is the blue line
y = 4/(3x) - 10.y is the red line
