which of the following are the correct properties of slope? check all that apply
A)the slope of a line that up from left to right is positive.
B)the slope of a line is always positive.
C)a steep line has negative slope.
D)some lines an undefined slope.
E)if two lines have the same slope, then they are the same line.
Answers
The correct statements among the options are: A) the slope of a line that rises from left to right is positive, and D) some lines have undefined slope.
A) the slope of a line that rises from left to right is positive: This statement is correct. The slope of a line is defined as the ratio of the rise (change in y) to the run (change in x). If a line rises from left to right, meaning the y-value increases as the x-value increases, then the slope is positive.
B) the slope of a line is always positive: This statement is incorrect. Slopes can be positive, negative, zero, or undefined, depending on the direction of the line and the values of the rise and run.
C) a steep line has negative slope: This statement is incorrect. A steep line, by definition, rises quickly, meaning that the y-value changes rapidly as the x-value increases. This corresponds to a positive slope. A negative slope would mean that the line goes down as x increases.
D) some lines have undefined slope: This statement is correct. If a line is vertical, meaning it does not change in x, then the slope is undefined. This is because the change in x is zero, and division by zero is undefined.
E) if two lines have the same slope, then they are the same line: This statement is incorrect. Two lines can have the same slope but still be different lines if they have different y-intercepts. The slope of a line gives information about the direction of the line, but the y-intercept gives information about the position of the line on the y-axis.
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