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How many variables does the equation y = 3x - 5 have? How many solutions does the equation y = 3x - 5 have? How could you show the solution(s) graphically? Are the lines parallel, perpendicular, or neither?

Option 1: 2 variables, infinite solutions, a straight line
Option 2: 2 variables, one solution, a curved line
Option 3: 1 variable, no solution, a straight line
Option 4: 1 variable, one solution, a straight line

User Rjgonzo
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1 Answer

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Final answer:

The equation y = 3x - 5 has two variables and infinitely many solutions, which can be graphically shown as a straight line on a graph. The line's slope is 3, given by the coefficient of 'x', and the y-intercept is -5.

Step-by-step explanation:

The equation y = 3x - 5 represents a linear equation, which means it contains two variables: 'x' is the independent variable and 'y' is the dependent variable. As it is a linear equation in two variables, it will have infinitely many solutions, each corresponding to a point on the line when graphed in a coordinate plane. The solution to this equation can be graphically represented by a straight line with a slope of 3, which is the coefficient of 'x', and a y-intercept of -5. This line graph is typically drawn with 'x' on the horizontal axis and 'y' on the vertical axis.

Regarding the orientation of the line, without another line to compare, we cannot directly determine if it is parallel or perpendicular. However, in general, two lines are parallel if they have the same slope, and they are perpendicular if the product of their slopes is -1. Therefore, we would need another line with a known slope to evaluate the relationship.

User Ryan Lue
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