To work with the equation \( 14x - 2y = 15 \), we can manipulate it to find \( y \) in terms of \( x \) or vice versa, or we can find specific values of \( x \) and \( y \) that satisfy the equation.
Solving for \( y \) in terms of \( x \):
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Start with the equation: \[ 14x - 2y = 15 \]
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Isolate the \( y \) term: \[ -2y = 15 - 14x \]
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Divide by -2 to solve for \( y \): \[ y = -\frac{15 - 14x}{2} \] \[ y = 7x - \frac{15}{2} \]
So, the equation in slope-intercept form (i.e., \( y = mx + b \)) is: \[ y = 7x - 7.5 \]
Finding specific solutions:
You can choose specific values for \( x \) and find the corresponding \( y \):
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If \( x = 0 \): \[ y = 7(0) - 7.5 = -7.5 \]
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If \( x = 1 \): \[ y = 7(1) - 7.5 = -0.5 \]
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If \( x = 2 \): \[ y = 7(2) - 7.5 = 7.5 \]
Graph of the Equation:
The line represented by the equation \( 14x - 2y = 15 \) has a slope of 7 and a y-intercept of -7.5. You can graph this line by plotting the points (0, -7.5), (1, -0.5), and (2, 7.5), then drawing a line through these points.
If you need additional information or a different form of the equation, please let me know!