2x - y - 3 = 0 in Slope-Intercept Form
The equation 2x - y - 3 = 0 is a linear equation in the standard form. To convert it into the slope-intercept form, we need to solve for y.
Standard Form to Slope-Intercept Form
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To convert the standard form to slope-intercept form, we need to isolate y on one side of the equation.
Converting 2x - y - 3 = 0 to Slope-Intercept Form
Let's start by adding y to both sides of the equation to get:
2x - y - 3 + y = 0 + y
This simplifies to:
2x - 3 = y
Now, we can divide both sides of the equation by -1 to get:
y = -2x + 3
And that's it! We have successfully converted the standard form to slope-intercept form.
Slope and Y-Intercept
Now that we have the equation in slope-intercept form, we can easily identify the slope (m) and y-intercept (b).
In this case, the slope (m) is -2, and the y-intercept (b) is 3.
Graphing the Line
Using the slope-intercept form, we can easily graph the line on a coordinate plane.
- Start by plotting the y-intercept (3) on the y-axis.
- From the y-intercept, use the slope (m) to find another point on the line. For example, if we go 1 unit to the right (x = 1), the y-coordinate will decrease by 2 units (y = 1). So, the point (1, 1) is also on the line.
- Draw a line through the two points to graph the equation.
And that's it! We have successfully converted the equation 2x - y - 3 = 0 to slope-intercept form and identified the slope and y-intercept.
