Final answer:
The slope-intercept form of the equation 4x-6y=12 is y=(2/3)x-2. The slope is 2/3 and the y-intercept is -2. The graph of this line is a straight line that slopes upwards and intersects the y-axis at -2.
Step-by-step explanation:
The equation 4x-6y=12 can be rewritten in slope-intercept form y=mx+b as follows:
Subtracting 4x from both sides: -6y = -4x+12
Dividing both sides by -6: y = (4/6)x - 2
Reducing the fraction: y = (2/3)x - 2
In this equation, the slope (m) is 2/3 and the y-intercept (b) is -2.
The slope represents the rate of change of y with respect to x, which means that for every increase of 1 in x, y increases by 2/3. '
The y-intercept is the point where the line intersects the y-axis, which in this case is (0, -2).
So therefore the graph of this line will have a slope of 2/3 and will intersect the y-axis at -2. It will be a straight line that starts below the y-axis (since the y-intercept is negative) and slopes upwards.