Final answer:
The equation x=y, when expressed in slope-intercept form, is written as y=x (option a), indicating a slope of 1 and a y-intercept of 0, which represents a line through the origin with a 45-degree angle to both axes. The correct answer is a) y=x.
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept.
The equation x=y can be rewritten in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Since x and y are equivalent, the slope (m) is 1, and there is no y-intercept value because the line passes through the origin, (0,0).
Therefore, the equation in slope-intercept form is y = x, which corresponds to option (a). This means the slope is 1 and the y-intercept is 0, indicating a straight line passing through the origin with an equal rise over run value.