Graph the equation 3๐ฅโ๐ฆ+ 3 = 0 on a Cartesian plane.
To graph the equation 3๐ฅ โ ๐ฆ + 3 = 0 on a Cartesian plane, we need to first rearrange the equation into the slope-intercept form ๐ฆ = ๐๐ฅ + ๐, where ๐ is the slope and ๐ is the y-intercept.
Let's start by isolating ๐ฆ on one side of the equation:
3๐ฅ โ ๐ฆ + 3 = 0
Subtract 3๐ฅ from both sides:
โ ๐ฆ = -3๐ฅ - 3
Multiply both sides by -1 to make the coefficient of ๐ฆ positive:
๐ฆ = 3๐ฅ + 3
Now we have the equation in slope-intercept form ๐ฆ = 3๐ฅ + 3, where the coefficient of ๐ฅ is the slope and the constant term 3 is the y-intercept.
To graph this equation, we can start by plotting the y-intercept, which is the point (0, 3) on the Cartesian plane.
Next, we can use the slope to find another point on the line. The slope of 3 means that for every 1 unit we move in the x-direction, we move 3 units in the y-direction. So, starting from the y-intercept (0, 3), we can move 1 unit to the right, and then 3 units up to find another point.
Plotting these two points, (0, 3) and (1, 6), we can draw a straight line passing through both points.
The final graph of the equation 3๐ฅ โ ๐ฆ + 3 = 0 on the Cartesian plane will be a straight line passing through the points (0, 3) and (1, 6).