y-intercept
The y-intercept is a key point on a graph of a linear equation. It is where the line crosses the y-axis. To find the y-intercept, set the value of x to 0 in the equation. For our example equation, which is \(\text{y=x-6}\), you simply substitute x with 0, giving you \(\text{y=0-6=-6}\). Thus, the y-intercept is the point \((0, -6)\). This point tells us that when x is 0, y is -6.
x-intercept
The x-intercept is another crucial point when graphing linear equations. It is where the line crosses the x-axis. To find the x-intercept, set the value of y to 0. In the equation \(\text{y=x-6}\), you substitute y with 0, which results in \(\text{0=x-6}\). Solving for x, you get \(\text{x=6}\). Therefore, the x-intercept is at \((6, 0)\). This point indicates that when y is 0, x is 6.
plotting points
Plotting points is an essential skill in graphing linear equations. Apart from the intercepts, you might want to plot additional points to ensure the accuracy of your graph. Select some x-values and solve for the corresponding y-values. For the equation \(\text{y=x-6}\), let's pick x-values like 1, 2, and 3:
- For \(\text{x=1}\), \(\text{y=1-6=-5}\) resulting in the point \((1, -5)\).
- For \(\text{x=2}\), \(\text{y=2-6=-4}\) resulting in the point \((2, -4)\).
- For \(\text{x=3}\), \(\text{y=3-6=-3}\) resulting in the point \((3, -3)\).
Plot these points on the coordinate plane along with your intercepts to draw a more accurate line.
linear equation
A linear equation is an equation that forms a straight line when graphed on a coordinate plane. The general format is \(\text{y=mx+b}\), where m is the slope and b is the y-intercept. In our example, \(\text{y=x-6}\), the slope (m) is 1 and the y-intercept (b) is -6. Linear equations depict a constant rate of change, meaning the slope remains the same across the entire line.
coordinate plane
The coordinate plane is a two-dimensional surface formed by two perpendicular lines called axes. The horizontal line is known as the x-axis, and the vertical line is called the y-axis. The point where they intersect is the origin, denoted as \((0,0)\). Each point on this plane is defined by a pair of coordinates \((x,y)\), where x represents the horizontal position and y represents the vertical position. When graphing a linear equation like \(\text{y=x-6}\), you plot points on this plane and connect them to form a straight line.
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