graph the equation by translating y=x
y=x+7
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
To graph the equation y = x + 7, we will follow these steps:
Step 1: Create a coordinate system by drawing two perpendicular lines that intersect at the origin (0,0).
Step 2: Identify the y-intercept by noting the constant term in the equation. In this case, the y-intercept is 7 because y = 7 when x = 0.
Step 3: Plot the y-intercept on the y-axis. The point will be (0, 7).
Step 4: Use the slope of 1 to find another point on the line. The slope indicates that for every 1 unit increase in x, there will be a 1 unit increase in y. So, starting from the y-intercept point (0, 7), go 1 unit to the right, and then go 1 unit up. This will give you the point (1, 8).
Step 5: Draw a straight line through the two points to represent the equation y = x + 7.
The graph of the equation y = x + 7 will be a straight line passing through the points (0, 7) and (1, 8).
To graph the equation y = x + 7, we need to understand the concept of translation in a coordinate plane.
The equation y = x represents a straight line passing through the origin with a slope of 1 (since the coefficient of x is 1). We can begin by plotting a few points on this line:
When x = -2, y = -2
When x = 0, y = 0
When x = 2, y = 2
Now, to translate this line up 7 units, we need to add 7 to the y-coordinate of each point:
When x = -2, y = -2 + 7 = 5
When x = 0, y = 0 + 7 = 7
When x = 2, y = 2 + 7 = 9
Plot these translated points on the coordinate plane. Connect these points to form a straight line.
The graph of the equation y = x + 7 should be a straight line with a positive slope passing through the point (0, 7).