Graph of y = 1/2x + 1
The graph of y = 1/2x + 1 is a line with a slope of 1/2 and a y-intercept of 1. The line passes through the points (0, 1) and (2, 2).
Equation of the line
The equation of the line can be written in slope-intercept form as y = 1/2x + 1.
Slope
The slope of the line is 1/2. This means that for every 1 unit increase in x, there is a 1/2 unit increase in y.
y-intercept
The y-intercept of the line is 1. This means that the line crosses the y-axis at the point (0, 1).
Plotting the line
To plot the line, we can use the following steps:
- Choose two values for x.
- Substitute these values into the equation of the line to find the corresponding values for y.
- Plot the points (x, y) on a coordinate plane.
For example, we can choose x = 0 and x = 2. Substituting these values into the equation of the line, we get the following points:
- (0, 1)
- (2, 2)
Plotting these points, we get the following line:
[Image of graph of y = 1/2x + 1]Additional questions and answers
- What is the slope of the line that is perpendicular to y = 1/2x + 1?
The slope of a line that is perpendicular to y = 1/2x + 1 is -2. This can be found using the fact that the product of the slopes of two perpendicular lines is equal to -1.
- What is the equation of the line that passes through the point (3, 4) and is parallel to y = 1/2x + 1?
The equation of the line that is parallel to y = 1/2x + 1 has the same slope of 1/2. The equation of this line can be written as y = 1/2x + b, where b is the y-intercept.
Substituting the point (3, 4) into this equation, we get the following equation:
4 = 1/2 * 3 + b
4 = 3/2 + b
b = 4 – 3/2
b = 5/2
Therefore, the equation of the line that passes through the point (3, 4) and is parallel to y = 1/2x + 1 is y = 1/2x + 5/2.
- What is the area of the triangle that is bounded by the line y = 1/2x + 1, the x-axis, and the line x = 2?
The area of a triangle is equal to 1/2 * base * height.
The base of the triangle is 2 units.
The height of the triangle is equal to the difference between the y-coordinates of the two points where the line y = 1/2x + 1 intersects the x-axis. These points are (0, 1) and (2, 2). Therefore, the height of the triangle is 2 – 1 = 1 unit.
Therefore, the area of the triangle is equal to
1/2 * 2 * 1 = 1 Therefore, the area of the triangle is 1 square unit.