Y 1/2x 1 Graph

Y = 1/2x + 1 Graph

The equation y = 1/2x + 1 is a linear equation that can be graphed as a line. The line has a slope of 1/2 and a y-intercept of 1.

To graph the line, we can use the following steps:

1. Find the y-intercept. This is the point where the line crosses the y-axis. In this case, the y-intercept is 1, so the line must pass through the point (0, 1).
2. Find the slope. The slope tells us how much the y-value changes for every change in the x-value. In this case, the slope is 1/2, so for every 1 unit we move to the right, we must move 2 units up.
3. Plot points. Using the y-intercept and the slope, we can plot points on the line. For example, if we move 1 unit to the right, we must also move 2 units up, so the next point on the line is (1, 3/2). If we move 2 units to the right, we must also move 4 units up, so the next point on the line is (2, 5/2).
4. Connect the points. Once we have plotted enough points, we can connect them to form a line.

The graph of y = 1/2x + 1 is shown below.

[Image of graph of y = 1/2x + 1]

Questions about y = 1/2x + 1 Graph

• What is the slope of the line?

The slope of the line is 1/2. This means that for every 1 unit we move to the right, we must move 2 units up.

• What is the y-intercept of the line?

The y-intercept of the line is 1. This means that the line crosses the y-axis at the point (0, 1).

• What is the equation of the line in slope-intercept form?

The equation of the line in slope-intercept form is y = 1/2x + 1.

• What is the x-intercept of the line?

The x-intercept of the line is the point where the line crosses the x-axis. To find the x-intercept, we set y to 0 and solve for x.

0 = 1/2x + 1 -1 = 1/2x -2 = x 

The x-intercept of the line is (-2, 0).

• What is the slope of the line that is perpendicular to y = 1/2x + 1?

The slope of the line that is perpendicular to y = 1/2x + 1 is -2. This is because the product of the slopes of two perpendicular lines is always equal to -1.

• What is the area of the triangle that is bounded by the line y = 1/2x + 1, the x-axis, and the y-axis?

The area of the triangle is equal to (1/2)(1)(1) = 1/2.

Additional Information

The line y = 1/2x + 1 can be used to represent a variety of real-world situations. For example, it can be used to represent the following:

• The relationship between the cost of a product and the number of units sold
• The relationship between the speed of a car and the time it takes to travel a certain distance
• The relationship between the amount of water in a tank and the time it takes to fill the tank

The line y = 1/2x + 1 is a simple but powerful tool that can be used to model a variety of real-world situations.