Question

What is the equation of the line that passes through the points (0,3/5)
, (−1/2,3/4)
?(1 point)
Responses

y=−3/10x+3/5
y is equal to negative 3 tenths x plus 3 fifths

y=3/5x−3/10
y is equal to 3 fifths x minus 3 tenths

y=−3/10x−3/5
y is equal to negative 3 tenths x minus 3 fifths

y=3/10x+3/5

Answer 1

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**