To find the equation of the line that passes through the points \((0, \frac{3}{5})\) and \((- \frac{1}{2}, \frac{3}{4})\), we can follow these steps:
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Find the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (0, \frac{3}{5})\) and \((x_2, y_2) = (-\frac{1}{2}, \frac{3}{4})\).
Substituting the values: \[ m = \frac{\frac{3}{4} - \frac{3}{5}}{-\frac{1}{2} - 0} \]
To calculate \(\frac{3}{4} - \frac{3}{5}\), we find a common denominator, which is 20: \[ \frac{3}{4} = \frac{15}{20}, \quad \frac{3}{5} = \frac{12}{20} \] Therefore: \[ \frac{3}{4} - \frac{3}{5} = \frac{15}{20} - \frac{12}{20} = \frac{3}{20} \]
Now substitute this into the slope formula: \[ m = \frac{\frac{3}{20}}{-\frac{1}{2}} = \frac{3}{20} \cdot -2 = -\frac{3}{10} \]
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Use point-slope form of a line equation where we can use one of the points, let's say \((0, \frac{3}{5})\): \[ y - y_1 = m(x - x_1) \] Substituting \(m = -\frac{3}{10}\), \(x_1 = 0\), and \(y_1 = \frac{3}{5}\): \[ y - \frac{3}{5} = -\frac{3}{10}(x - 0) \] This simplifies to: \[ y - \frac{3}{5} = -\frac{3}{10}x \] Now add \(\frac{3}{5}\) to both sides: \[ y = -\frac{3}{10}x + \frac{3}{5} \]
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Convert \(\frac{3}{5}\) to a decimal: \(\frac{3}{5} = 0.6\)
Therefore, the equation of the line is: \[ y = -\frac{3}{10}x + 0.6 \]
Now, looking at the provided responses, the equation that matches this line is:
y is equal to negative 3 tenths x plus 3 fifths.