What is the slope and y-intercept of the equation y=x?
Understand the Problem
The question is about identifying the key characteristics of the equation y=x based on the slope and y-intercept. We need to determine which of the options correctly describes these characteristics.
Answer
Slope: $1$, Y-intercept: $0$.
Answer for screen readers
The correct characteristics of the equation are: Slope: $1$, Y-intercept: $0$.
Steps to Solve
- Identify the equation characteristics
The equation $y = x$ is in slope-intercept form, which is $y = mx + b$ where $m$ represents the slope and $b$ represents the y-intercept.
- Determine the slope
The coefficient in front of $x$ in the equation $y = x$ is $1$. Therefore, the slope $m$ is $1$.
- Determine the y-intercept
The y-intercept is the constant term in the equation when $x = 0$. In $y = x$, if we set $x = 0$, we get $y = 0$. Thus, the y-intercept $b$ is $0$.
- Summarize the characteristics
So, for the equation $y = x$, the slope is $1$ and the y-intercept is $0$.
The correct characteristics of the equation are: Slope: $1$, Y-intercept: $0$.
More Information
The line represented by the equation $y = x$ has a positive slope of $1$, meaning it rises one unit on the y-axis for every unit it moves to the right on the x-axis. The line crosses the y-axis at the origin (0, 0).
Tips
- Confusing the slope with the y-intercept. The slope is the number in front of $x$, while the y-intercept is the constant term.
- Miscalculating the y-intercept when using different forms of the equation.
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