The equation of a straight line if expressed as y = mx + c, gives the slope as m
For y = 4x + 12, the slope is 4. As it is positive the y values of the line increase with the x values
For y = -2x/3 + 4, the slope is -2/3. As it is negative, the y values decrease as the x values increase.
The equation for a line is
y = mx + b
In this equation, the variable "m" stands for the slope of the line. By looking at the equations you give, you can clearly see the slope.
For the first line, the slope is 4. This means that the line will go up 4 units for every 1 unit it goes to the right.
The slope of the second line is -2/3. This means that the line will go down 2 units for every 3 units it goes to the right.
We notice that the given equation are written in slope intercept form.
y=mx + n
m represents the slope and n represents the y intercept.
y = 4x + 12
The slope of this line is m=4. This means that y increases 4 units for every 1 unit of x.
y = -2x/3 + 4
The slope of this line is m=-2/3. This means that y decreases 2 units for every 3 unit of x.