In mathematics, a line is represented by an equation which contains two variables – x and y. The slope of the line is the rate of change of the y-values with respect to the x-values. The y-intercept of the line is the point at which the line intersects the y-axis. In this article, we will discuss which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2.
Determining Slope and Y-Intercept of a Line
The slope of a line is determined by the equation m = (y2 – y1) / (x2 – x1). The y-intercept of a line is determined by the equation b = y – mx, where m is the slope of the line.
For the line y = x – 2, the slope is m = 1 and the y-intercept is b = -2.
Examining the Graph for Y = X – 2
The graph of the equation y = x – 2 is a straight line that passes through the origin (0, 0) and has a slope of 1 and a y-intercept of -2. The graph is shown below.
The graph shows that for each increase of 1 in the x-value, the y-value increases by 1. This confirms that the slope of the line is 1 and the y-intercept is -2.
In conclusion, the graph of the equation y = x – 2 is the graph that represents a line with a slope of and a y-intercept equal to that of the line y = x – 2.
