-with-a-slope-of-2%2F3.jpeg "(0 3) With A Slope Of 2/3")
The Line (0, 3) with a Slope of 2/3
In this article, we will explore the properties and characteristics of a line that passes through the point (0, 3) with a slope of 2/3.
What is the Slope-Intercept Form?
The slope-intercept form of a linear equation is given by the formula:
y = mx + b
where m is the slope and b is the y-intercept.
Finding the Equation of the Line
Since we are given that the line passes through the point (0, 3) with a slope of 2/3, we can write the equation of the line as:
y = (2/3)x + b
To find the value of b, we can substitute the point (0, 3) into the equation:
3 = (2/3)(0) + b
3 = b
So, the equation of the line is:
y = (2/3)x + 3
Graphing the Line
To graph the line, we can start by plotting the y-intercept, which is at (0, 3). Then, we can use the slope to find another point on the line. For example, if we move 3 units to the right, the slope tells us that we should move 2 units up. This gives us the point (3, 5).
Properties of the Line
- The line has a slope of 2/3, which means that it rises 2 units for every 3 units it runs to the right.
- The line passes through the point (0, 3), which means that it has a y-intercept of 3.
- The line has an x-intercept of 9, which can be found by setting y = 0 and solving for x.
Conclusion
In conclusion, the line (0, 3) with a slope of 2/3 has an equation of y = (2/3)x + 3, and it passes through the point (0, 3) with a slope of 2/3. We can graph the line by plotting the y-intercept and using the slope to find another point on the line. The line has several important properties, including its slope, y-intercept, and x-intercept.
