Y - intercept/X - intercept:
when talking about y-intercept, you are finding where x = 0, and when finding the x-intercept, you are finding where y = 0.
Here, the y-intercept is -3 (look where x is 0)
Slope:
To find the slope, take any 2 points and use the equation:
Y2 - Y1
————— = m; m is the slope.
X2 - X1
As an example, I will take (1, -1) and (2, 1).
Y2 = 1
Y1 = -1
X2 = 2
X1 = 1
1 - (-1) 1+ 1
————— = ————— = 2/1 = 2
2 - 1 1
2 is the slope.
Or, observe how y always increases by 2 for every x (rise/run)
Equation:
Now, since we found the slope (2) and the y intercept, simply plug in the numbers into the linear equation form (y = mx + b). You should know that m means the slope and b means the y intercept. Meaning the equation is...
y = 2x - 3
Hope it helped :)