Graph the equation and identify the y intercept y= 3/2x -4.
Thank you.
To graph the equation y = (3/2)x - 4 and identify the y-intercept, you can follow these steps:
1. Identify the slope and y-intercept:
- The coefficient of x in the equation is 3/2, which is the slope.
- The constant term -4 is the y-intercept.
2. Plot the y-intercept:
- The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.
- Substitute x = 0 into the equation to find the y-coordinate.
- For y = (3/2)(0) - 4, simplify to y = -4.
- So, the y-intercept is the point (0, -4).
3. Use the slope to find additional points on the line:
- The slope of 3/2 indicates that for every 2 units of horizontal change (increase in x), the line goes up 3 units (change in y).
- You can apply this information to find other points on the line.
- For example, if you move 2 units to the right from the y-intercept (0, -4), you increase x by 2: x = 0 + 2.
- Substitute the new x-value into the equation: y = (3/2)(2) - 4.
- Simplify to find y = 1. You get the point (2, 1).
4. Plot the points and draw a line:
- Plot the y-intercept (0, -4) and any additional points you found (e.g., (2, 1)).
- Draw a straight line passing through these points.
So, the graph of the equation y = (3/2)x - 4 will be a straight line that passes through the points (0, -4) and (2, 1).