graph the equation by translating y=x

Question

y=x+7

Answer 1

To graph the equation y=x+7, we can follow these steps:

1. Start with the graph of y=x, which is a straight line passing through the origin at (0,0) and making a 45-degree angle with both the x and y axis. This is a diagonal line with a slope of 1.

2. Now, we need to translate the line upward along the y-axis by 7 units. So, we move every point on the line y=x upwards by 7 units.

For example, the point (0,0) on the line y=x will be moved to the point (0,7). Similarly, the point (1,1) on the line y=x will be moved to the point (1,8), and so on.

3. After moving all the points upward by 7 units, we obtain the graph of the equation y=x+7. This is also a straight line with a slope of 1, but it passes through the point (0,7) on the y-axis.

You can plot these points on a graph and draw the line passing through them to visualize the equation y=x+7. Here's a link to a graph of the equation: https://www.desmos.com/calculator/mfhrcd1ugv