When studying linear equations, it is important to understand the concept of slope and y-intercept. Knowing the slope of a line can help you determine its steepness and direction, while the y-intercept can help you determine where the line crosses the y-axis. In this article, we will explore which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2.
Determining Slope of Line
The slope of a line is often represented by the letter “m”, and is the ratio of the change in the y-values divided by the change in the x-values. The slope of the line y = x – 2 can be determined by calculating the difference between two points on the line. For example, if we take the points (3,1) and (5,3), the difference in the y-values is 2 and the difference in the x-values is 2. Therefore, the slope of the line is 2/2, or 1.
Examining Y-Intercept of Line
The y-intercept of a line is the point at which the line crosses the y-axis. To determine the y-intercept of the line y = x – 2, we need to find the point at which the line crosses the y-axis. To do this, we can plug in 0 for the x-value and solve for y. In this case, if we plug in 0 for the x-value, the equation becomes y = 0 – 2, which simplifies to y = -2. Therefore, the y-intercept of the line is -2.
The graph of a line with a slope of 1 and a y-intercept of -2 will look like a straight line that is sloping up from left to right. The line will cross the y-axis at the point (-2,0).
In conclusion, understanding the slope and y-intercept of a line can be helpful in determining its shape and position. In this article, we have explored the line y = x – 2 and determined that the slope of the line is 1 and the y-intercept is -2. We have also determined that the graph of this line will be a straight line that is sloping up from left to right and crossing the y-axis at the point (-2,0).