Which Equation Represents A Line That Passes Through The Two Points In The Table?${ \begin{tabular}{|c|c|} \hline X X X & Y Y Y \ \hline 3 & 1 \ \hline 6 & 6 \ \hline \end{tabular} }$A. { Y - 6 = \frac{3}{5}(x - 6) $}$ B. [$
Which Equation Represents a Line That Passes Through the Two Points in the Table?
In mathematics, the concept of a line is a fundamental idea that is used to describe a set of points that extend infinitely in two directions. A line can be represented graphically on a coordinate plane, and it can also be described algebraically using an equation. In this article, we will explore the concept of a line and how it can be represented using an equation.
The problem asks us to determine which equation represents a line that passes through the two points in the table. The table contains two points, (3, 1) and (6, 6), and we need to find the equation of the line that passes through these two points.
The equation of a line can be represented in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is a measure of how steep the line is, and it can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
To calculate the slope of the line that passes through the two points in the table, we can use the formula m = (y2 - y1) / (x2 - x1). Plugging in the values from the table, we get:
m = (6 - 1) / (6 - 3) m = 5 / 3 m = 1.67
Now that we have the slope of the line, we can write the equation of the line in the form of y = mx + b. We can use either of the two points in the table to find the value of b. Let's use the point (3, 1):
1 = (5/3)(3) + b 1 = 5 + b b = -4
Now that we have the values of m and b, we can write the equation of the line:
y = (5/3)x - 4
The problem provides two equations, A and B, and asks us to determine which one represents the line that passes through the two points in the table. Let's compare the two equations:
A. y - 6 = (3/5)(x - 6) B. y = (5/3)x - 4
To simplify equation A, we can expand the right-hand side:
y - 6 = (3/5)(x - 6) y - 6 = (3/5)x - 18/5 y = (3/5)x - 18/5 + 6 y = (3/5)x - 18/5 + 30/5 y = (3/5)x + 12/5
Now that we have simplified equation A, we can compare it to equation B:
A. y = (3/5)x + 12/5 B. y = (5/3)x - 4
Based on the comparison of the two equations, we can conclude that equation B represents the line that passes through the two points in the table.
The final answer is B.
Which Equation Represents a Line That Passes Through the Two Points in the Table? - Q&A
In our previous article, we explored the concept of a line and how it can be represented using an equation. We also determined that the equation y = (5/3)x - 4 represents the line that passes through the two points in the table. In this article, we will answer some frequently asked questions related to the topic.
A: The slope of the line that passes through the two points in the table is 5/3.
A: To calculate the slope of a line, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
A: The equation of the line that passes through the two points in the table is y = (5/3)x - 4.
A: To write the equation of a line in the form of y = mx + b, you need to know the slope (m) and the y-intercept (b). You can use either of the two points in the table to find the value of b.
A: The y-intercept of the line that passes through the two points in the table is -4.
A: To compare two equations, you can simplify them and then compare the coefficients of the variables. If the coefficients are the same, then the equations represent the same line.
A: The two equations A and B are different. Equation A is y = (3/5)x + 12/5, while equation B is y = (5/3)x - 4. Equation B represents the line that passes through the two points in the table.
A: To determine which equation represents a line that passes through two points, you need to compare the equations and simplify them. You can also use the formula m = (y2 - y1) / (x2 - x1) to calculate the slope of the line and then use it to write the equation of the line.
In this article, we answered some frequently asked questions related to the topic of determining which equation represents a line that passes through two points. We hope that this article has been helpful in clarifying any doubts that you may have had.
The final answer is B.