Question

#7-9 graph the equation

1. $y = \frac{5}{3}x$

#10-12 c

Explanation:

Step1: Identify the form of the equation

The equation \( y = \frac{5}{3}x \) is in the slope - intercept form \( y=mx + b \), where \( m=\frac{5}{3} \) (the slope) and \( b = 0 \) (the y - intercept). So the line passes through the origin \((0,0)\).

Step2: Find another point using the slope

The slope \( m=\frac{\text{rise}}{\text{run}}=\frac{5}{3} \). Starting from the origin \((0,0)\), if we move 3 units to the right (run = 3, since run is positive in the x - direction) and 5 units up (rise = 5, since slope is positive), we get the point \((0 + 3,0+5)=(3,5)\). We can also use a negative run and rise. If we move 3 units to the left (run=-3) and 5 units down (rise = - 5), we get the point \((0-3,0 - 5)=(-3,-5)\).

Step3: Plot the points and draw the line

Plot the points \((0,0)\) and \((3,5)\) (or \((-3,-5)\)) on the coordinate plane. Then draw a straight line passing through these points. The line should have a positive slope, passing through the origin, and passing through \((3,5)\) and \((-3,-5)\) (and other points that satisfy \( y=\frac{5}{3}x \) like \((6,10)\) or \((-6,-10)\) if we extend the line).

Answer:

To graph \( y=\frac{5}{3}x \):

1. Plot the y - intercept: Since \( b = 0 \), plot the point \((0,0)\).
2. Use the slope \( m=\frac{5}{3}\): From \((0,0)\), move 3 units right and 5 units up to plot \((3,5)\), or 3 units left and 5 units down to plot \((-3,-5)\).
3. Draw a straight line through the plotted points. The line passes through \((0,0)\), \((3,5)\), \((-3,-5)\) and extends infinitely in both directions.