Question

graph the line.
$y = \frac{3}{2}x$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{3}{2}x \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{3}{2} \) (slope) and \( b = 0 \) (y - intercept). So the line passes through the origin \((0,0)\).

Step2: Use the slope to find another point

The slope \( m=\frac{3}{2}=\frac{\text{rise}}{\text{run}} \). From the point \((0,0)\), we rise 3 units (up) and run 2 units (to the right). So we get the point \((0 + 2,0+3)=(2,3)\). We can also go in the opposite direction: from \((0,0)\), rise - 3 units (down) and run - 2 units (to the left) to get the point \((- 2,-3)\).

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((2,3)\) (and/or \((-2,-3)\)) on the coordinate plane and then draw a straight line passing through these points.

Answer:

To graph \( y=\frac{3}{2}x \), plot the origin \((0,0)\). Then use the slope \( \frac{3}{2} \) to find another point: from \((0,0)\), move 2 units right and 3 units up to get \((2,3)\) (or 2 units left and 3 units down to get \((-2,-3)\)). Draw a straight line through these points.