To find the equation of the line that passes through the two points \((0, \frac{3}{5})\) and \((- \frac{1}{2}, \frac{3}{4})\), we first need to determine the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let point 1 be \((x_1, y_1) = (0, \frac{3}{5})\) and point 2 be \((x_2, y_2) = (-\frac{1}{2}, \frac{3}{4})\).
Substituting the values into the slope formula:
\[ m = \frac{\frac{3}{4} - \frac{3}{5}}{-\frac{1}{2} - 0} \]
To subtract \(\frac{3}{4}\) and \(\frac{3}{5}\), we need a common denominator. The least common multiple of 4 and 5 is 20.
Converting \(\frac{3}{4}\) and \(\frac{3}{5}\):
\[ \frac{3}{4} = \frac{15}{20}, \quad \frac{3}{5} = \frac{12}{20} \]
Now, substituting these values into the slope formula:
\[ m = \frac{\frac{15}{20} - \frac{12}{20}}{-\frac{1}{2}} = \frac{\frac{3}{20}}{-\frac{1}{2}} = \frac{3}{20} \cdot -2 = -\frac{3}{10} \]
Now that we have the slope, we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
Using the point \((0, \frac{3}{5})\) and the slope \(m = -\frac{3}{10}\):
\[ y - \frac{3}{5} = -\frac{3}{10}(x - 0) \]
Simplifying this:
\[ y - \frac{3}{5} = -\frac{3}{10}x \]
Adding \(\frac{3}{5}\) to both sides:
\[ y = -\frac{3}{10}x + \frac{3}{5} \]
Thus, the equation of the line is:
\[ y = -\frac{3}{10}x + \frac{3}{5} \]
So the correct response is:
y = −3/10x + 3/5