Question

What is the equation of the line that passes through the points (0, 3/5) , (−1/2, 3/4) ?(1 point) Responses y=−310x+35 y is equal to negative 3 tenths x plus 3 fifths y=35x−310 y is equal to 3 fifths x minus 3 tenths y=−310x−35 y is equal to negative 3 tenths x minus 3 fifths y=310x+35

Answer 1

To find the equation of the line that passes through the points \((0, \frac{3}{5})\) and \((- \frac{1}{2}, \frac{3}{4})\), we will first find the slope \(m\) of the line:

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the given points \((0, \frac{3}{5})\) and \((- \frac{1}{2}, \frac{3}{4})\):

- \(x_1 = 0\), \(y_1 = \frac{3}{5}\)
- \(x_2 = -\frac{1}{2}\), \(y_2 = \frac{3}{4}\)

Now we calculate the slope:

\[
m = \frac{\frac{3}{4} - \frac{3}{5}}{-\frac{1}{2} - 0}
\]

To do \(\frac{3}{4} - \frac{3}{5}\), we need a common denominator. The least common multiple of 4 and 5 is 20. So, we can convert the fractions:

\[
\frac{3}{4} = \frac{15}{20}, \quad \frac{3}{5} = \frac{12}{20}
\]

Thus,

\[
\frac{3}{4} - \frac{3}{5} = \frac{15}{20} - \frac{12}{20} = \frac{3}{20}
\]

Next, substituting back into our slope equation gives:

\[
m = \frac{\frac{3}{20}}{-\frac{1}{2}} = \frac{3}{20} \cdot \left(-2\right) = -\frac{3}{10}
\]

Now we have the slope \(m = -\frac{3}{10}\).

Next, we can use the point-slope form of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

Using the point \((0, \frac{3}{5})\):

\[
y - \frac{3}{5} = -\frac{3}{10}(x - 0)
\]

This simplifies to:

\[
y - \frac{3}{5} = -\frac{3}{10}x
\]

Adding \(\frac{3}{5}\) to both sides:

\[
y = -\frac{3}{10}x + \frac{3}{5}
\]

Now, we can express \(\frac{3}{5}\) with a denominator of 10:

\[
\frac{3}{5} = \frac{6}{10}
\]

So, the final equation of the line is:

\[
y = -\frac{3}{10}x + \frac{6}{10}
\]

Thus, the correct response among the options given is:

**y = -\frac{3}{10}x + \frac{3}{5}** which is equivalent to
**y = -\frac{3}{10}x + 0.6**.