Solve for y and graph the equation with a standard window on a graphing utility.

Question

5x-3y=5

Answer 1

To solve for \( y \) in the equation \( 5x - 3y = 5 \), follow these steps:

1. Start with the original equation: \[ 5x - 3y = 5 \]

2. Isolate \( y \) by moving \( 5x \) to the other side: \[ -3y = 5 - 5x \]

3. Divide everything by \(-3\) to solve for \( y \): \[ y = \frac{5 - 5x}{-3} \] Simplifying gives: \[ y = -\frac{5}{3} + \frac{5}{3}x \]

Thus, the equation in slope-intercept form is: \[ y = \frac{5}{3}x - \frac{5}{3} \]

Now, we can identify the slope \( m = \frac{5}{3} \) and the y-intercept \( b = -\frac{5}{3} \).

Graphing the Equation

1. Identify Points:

   • Y-intercept: When \( x = 0 \), \( y = -\frac{5}{3} \) (approximately -1.67)
   • X-intercept: Set \( y = 0 \) in the original equation to find: \[ 5x - 3(0) = 5 \implies 5x = 5 \implies x = 1 \] So the x-intercept is \( (1, 0) \).

2. Plot Points:

   • Plot the points \( (0, -\frac{5}{3}) \) and \( (1, 0) \).

3. Draw the Line: Use a ruler to draw a straight line through the two points.

Using a Graphing Utility

To graph it on a graphing utility:

1. Enter the equation in the form: \[ y = \frac{5}{3}x - \frac{5}{3} \]

2. Set the window to a standard setting that includes both intercepts and additional space:

   • \( x \) range: -5 to 5
   • \( y \) range: -5 to 5

3. Graph the function to visualize the line.

This will give you the graphical representation of the equation \( 5x - 3y = 5 \).