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A system of equations is graphed on the grid. The coordinates of the points on the graph are as follows:

(1, 5)
(-4, 4)
(-1, 3)
(2, 13)
(-1, -2)

Which system of equations does the graph represent? Please provide the equations of the lines that correspond to this graph."

1 Answer

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Final answer:

The system of equations represented by the points given is composed of two lines with equations y = 8x - 3 and y = -1/3x + 10/3, derived by calculating slopes and y-intercepts from the coordinates provided.

Step-by-step explanation:

To determine which system of equations a graph represents, especially for a linear system, we need to find the equations of the lines represented by the coordinates given. To find the equation of a line, we use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Given the coordinates (1, 5), (-4, 4), (-1, 3), (2, 13), and (-1, -2), we can form two apparent pairs that would lie on the same line: (1, 5) and (2, 13), and (-4, 4) and (-1, 3). It seems there might be a typo since the last coordinate, (-1, -2), does not align with the pattern of the other coordinates.

To find the first line's equation, we first calculate the slope (dependence of y on x) using the formula m = (y2 - y1) / (x2 - x1), resulting in m = (13 - 5) / (2 - 1), which simplifies to m = 8. Hence, the line through (1, 5) and (2, 13) has a slope of 8. Then we use one of the points to solve for b, giving us the equation y = 8x + b. Plugging point (1, 5) into the equation yields 5 = 8(1) + b, leading to b = -3. So, the first line's equation is y = 8x - 3.

Applying the same process to the second pair of points, (-4, 4) and (-1, 3), we calculate the slope m = (3 - 4) / (-1 + 4) and find that m = -1/3. Using the point (-1, 3), we get 3 = (-1/3)(-1) + b, which simplifies to b = 10/3. Thus, the second line's equation is y = -1/3x + 10/3.

Therefore, the system of equations represented by the points, considering the potential typo, would be comprised of the lines y = 8x - 3 and y = -1/3x + 10/3.

User Dhiren Basra
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