1.What is the standard form of a linear equation?A.x+y=0
B.y= MX+b
C. m=rise/run
D. ax +By=C
2.Which term could be used to describe the graph of a line on a coordinate plane?
A. independent variable
B. test points
C. set of all solutions
D. dependent variable
3.Explain whether the points (−13,4), (−7,3), (−1,2), (5,1), (11,0), (17,−1) represent the set of all the solutions for the equation y=−1/6x+11/6.
A.Yes, because all the solutions of y=−1/6x+11/6 need to be integer values for x and y.
B.No, because the point (17,−1) is not on the line that represents the equation y=−1/6x+11/6.
C.No, because the set of all solutions of y=−1/6x+11/6 is represented by the line of the equation.
D. Yes, because all of the points that are listed are on the line y=−1/6x+11/6.
Answer them all in one answer please and thank you.
1. The standard form of a linear equation is "D. ax + By = C". This form represents a linear equation with the x and y variables, where "a" and "b" are coefficients, and "C" is a constant term.
To determine the standard form of a linear equation, you can start with an equation in a different form, such as slope-intercept form (y = mx + b), point-slope form ((y - y1) = m(x - x1)), or other variations. Then, by rearranging terms and simplifying, you can convert it to the standard form ax + By = C.
2. The term that could be used to describe the graph of a line on a coordinate plane is "C. set of all solutions."
A line on a coordinate plane represents all the points that satisfy the given equation. These points can be thought of as solutions to the equation because their coordinates satisfy the relationship expressed by the equation. Therefore, the graph of a line represents the set of all solutions to the equation.
3. The correct explanation is "C. No, because the set of all solutions of y=−1/6x+11/6 is represented by the line of the equation."
The given equation y=−1/6x+11/6 represents a linear relationship between x and y, with a slope of -1/6 and a y-intercept of 11/6. The points listed in the question, (−13,4), (−7,3), (−1,2), (5,1), (11,0), (17,−1), correspond to the coordinates (x, y) on this line.
Since each of these points satisfies the equation when substituted into it, they do indeed represent solutions to the equation. Therefore, the set of all solutions of y=−1/6x+11/6 is represented by the line described by the equation. Thus, the correct explanation is that the given points do not represent the set of all solutions; instead, the line itself (corresponding to the equation y=−1/6x+11/6) represents the set of all solutions.