Question

12. Which equation represents the graph? (1 point) Responses y=3x+5 y is equal to 3 x plus 5 y=5/4x+3 y is equal to 5 fourths x plus 3 y=−4/5x+3 y is equal to negative 4 fifths x plus 3 y=1/2x−1 y is equal to 1 half x minus 1

this is whats on the graph (0, 2) (5, -1)

Answer 1

heres the answers
y=3x+5 y is equal to 3 x plus 5 y=5/4x+3 y is equal to 5 fourths x plus 3 y=−4/5x+3 y is equal to negative 4 fifths x plus 3 y=1/2x−1 y is equal to 1 half x minus 1

Answer 2

To find the equation of the line that passes through the points (0, 2) and (5, -1), we can start by calculating the slope (m) of the line. The slope is given by the formula:

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

Here, we can take (x1, y1) = (0, 2) and (x2, y2) = (5, -1).

Calculating the slope:

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

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

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

Substituting in one of the points and the slope we calculated:

\[
y - 2 = -\frac{3}{5}(x - 0)
\]

This simplifies to:

\[
y - 2 = -\frac{3}{5}x
\]
\[
y = -\frac{3}{5}x + 2
\]

Now we can check which of the given responses matches this equation.

We recognize that we need to rewrite the equation in a form that matches one of the available choices. The choices listed do not include \(y = -\frac{3}{5}x + 2\), indicating that the correct equation may not have been provided in the responses.

It's possible to approximate the line equation based on the calculated slope \(-\frac{3}{5}\), but that doesn't clearly match any response given.

If we consider the original points, \(y=2\) is already the y-intercept when \(x=0\). At \(x=5\), we computed y as -1, which confirms our calculations are correct.

None of the supplied options appear to fit, indicating there may be an error in provided choices. Please double-check the corresponding responses to ensure they correspond to the determined slope and y-intercept.

Answer 3

Thank you for sharing the options. Given the points (0, 2) and (5, -1), let's find the correct equation step-by-step once more.

1. **Calculate the slope (m)** between the points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 2}{5 - 0} = \frac{-3}{5}
\]

2. **Use the slope to find the equation of the line** using the point-slope form equation:
- Using the point (0, 2), we have:
\[
y - 2 = -\frac{3}{5}(x - 0)
\]
Which simplifies to:
\[
y = -\frac{3}{5}x + 2
\]

Now let's see if this equation corresponds to the options provided:

1. **y = 3x + 5** (a slope of 3, which does not match)
2. **y = \frac{5}{4}x + 3** (a slope of \(\frac{5}{4}\), which does not match)
3. **y = -\frac{4}{5}x + 3** (a slope of \(-\frac{4}{5}\), which does not match)
4. **y = \frac{1}{2}x - 1** (a slope of \(\frac{1}{2}\), which does not match)

None of the given equations match the slope \(-\frac{3}{5}\) and y-intercept of 2 we derived.

Based on all calculations, the correct equation does not appear to be included in the answer choices provided. If you can double-check for any potential errors or if there are any missing options, please let me know!