Question
Two streets are parallel on a map, 7th street and 8th street. The map is put on a coordinate plane and the equation for 7th street is 𝑦 = 2𝑥 − 6. 8th street goes through the coordinates (1,3) on the map. Write an equation of the line 8th street is on.(1 point) Responses 8th Street is on y=2x+1 8th Street is on y is equal to 2 x plus 1 8th Street is on y=2x+3 8th Street is on y is equal to 2 x plus 3 8th Street is on y=−12x+1 8th Street is on y is equal to negative 1 half x plus 1 8th Street is on y=−12x+72
Answers
GPT-4o mini
Since 7th Street has the equation \( y = 2x - 6 \) and 8th Street is parallel to 7th Street, it will have the same slope. The slope of the line \( y = 2x - 6 \) is 2.
To find the equation of 8th Street, we can use the point-slope form of a line equation. Given that 8th Street passes through the coordinate (1, 3):
1. Start with the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point (1, 3) and \( m \) is the slope (which is 2).
2. Plugging in the values:
\[
y - 3 = 2(x - 1)
\]
3. Simplify the equation:
\[
y - 3 = 2x - 2
\]
\[
y = 2x + 1
\]
Thus, the equation for 8th Street is \( y = 2x + 1 \).
The correct responses for the equation of 8th Street are:
- 8th Street is on \( y=2x+1 \)
- 8th Street is on \( y \text{ is equal to } 2 x + 1 \)
To find the equation of 8th Street, we can use the point-slope form of a line equation. Given that 8th Street passes through the coordinate (1, 3):
1. Start with the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point (1, 3) and \( m \) is the slope (which is 2).
2. Plugging in the values:
\[
y - 3 = 2(x - 1)
\]
3. Simplify the equation:
\[
y - 3 = 2x - 2
\]
\[
y = 2x + 1
\]
Thus, the equation for 8th Street is \( y = 2x + 1 \).
The correct responses for the equation of 8th Street are:
- 8th Street is on \( y=2x+1 \)
- 8th Street is on \( y \text{ is equal to } 2 x + 1 \)