Question

Which equation represents the graph?
Graph points: (0,3) (5,-1)


(1 point)
Responses

y=54x+3
y is equal to 5 fourths x plus 3

y=−45x+3
y is equal to negative 4 fifths x plus 3

y=12x−1
y is equal to 1 half x minus 1

y=3x+5
y is equal to 3 x plus 5
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Answer 1

To find the equation of the line represented by the points (0, 3) and (5, -1), we can use the slope-intercept form of a line, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. **Find the slope (\( m \))**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 3) and (5, -1):
\[
m = \frac{-1 - 3}{5 - 0} = \frac{-4}{5} = -\frac{4}{5}
\]

2. **Find the y-intercept (\( b \))**:
We know from the point (0, 3) that when \( x = 0 \), \( y = 3 \). Therefore, the y-intercept \( b \) is 3.

3. **Write the equation**:
Now we can substitute the values of \( m \) and \( b \) into the slope-intercept form:
\[
y = -\frac{4}{5}x + 3
\]

Now we can check which of the provided response options matches this equation:

- The corresponding response is:
**y = -\frac{4}{5}x + 3**, which we can also read as:
**y is equal to negative 4 fifths x plus 3**.

So the correct answer is:
**y is equal to negative 4 fifths x plus 3**.