Question

y = \frac{4}{3}x + 2
answer
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Explanation:

Step1: Find the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=\frac{4}{3}x + 2\), when \(x = 0\), we substitute \(x = 0\) into the equation:
\(y=\frac{4}{3}(0)+2=2\). So one point on the line is \((0,2)\).

Step2: Find another point using the slope

The slope \(m=\frac{4}{3}\), which means for a run of \(3\) (change in \(x\)), the rise is \(4\) (change in \(y\)). Starting from the point \((0,2)\), if we add \(3\) to the \(x\) - coordinate (\(x=0 + 3=3\)) and add \(4\) to the \(y\) - coordinate (\(y = 2+4 = 6\)), we get the point \((3,6)\).

We can also find a point with a negative \(x\) - value. If we take \(x=- 3\), then \(y=\frac{4}{3}(-3)+2=-4 + 2=-2\), so the point \((-3,-2)\) is also on the line.

To graph the line \(y = \frac{4}{3}x+2\), we can plot the points \((0,2)\) and \((3,6)\) (or \((-3,-2)\) and \((0,2)\)) and then draw a straight line through them.

(Note: Since the problem is about graphing, the key is to identify two points on the line. The process above shows how to find two points to plot.)

Answer:

To graph \(y=\frac{4}{3}x + 2\), plot the points \((0,2)\) (y - intercept) and \((3,6)\) (using slope \(\frac{4}{3}\): from \((0,2)\), move 3 units right and 4 units up) or \((-3,-2)\) (from \((0,2)\), move 3 units left and 4 units down) and draw a line through them.