No. In a linear equation, y = mx + b, the slope is m, and the x intercept is where mx + b = 0.
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x-3y=3 is the same as -3y=-x+3 and now divide by -3 and you have y=(1/3)x-1 which is the slope intercept form.
y - x = 0 which is the same as y = x + 0 which is of the form y = mx + c where m is the slope and c is the intercept. Hence for y = x + 0, the slope is 1 ans the intercept is 0. The equation represents a line making 45 degrees to the a-axis and it passes through the origin.
y = {slope}x + {y intercept}
x
The slope of x and the y intercept as for example in the straight line equation of y = 2x+3 the slope is 2 and the y intercept is 3