On a map, Peach Street is modeled by the equation 4x−y=7 . Apple Street is perpendicular to Peach Street and passes through the point (12, 2) . Find the equation that models Apple Street.(1 point)
Responses
y=14x+5
y equals 1 fourth x plus 5
y=−14x−1
y equals negative 1 fourth x minus 1
y=14x−1
y equals 1 fourth x minus 1
y=−14x+5
To find the equation for Apple Street, we need to determine the slope of Peach Street and then find the negative reciprocal of that slope, since the two streets are perpendicular.
The equation for Peach Street is given by 4x - y = 7. We can rearrange this equation to solve for y:
y = 4x - 7.
From this equation, we can see that the slope of Peach Street is 4.
Since Apple Street is perpendicular to Peach Street, the slope of Apple Street will be the negative reciprocal of 4, which is -1/4.
Now we can use the point-slope form of a linear equation to find the equation of Apple Street. The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) is a point on the line and m is the slope.
Using the given point (12, 2) and the slope -1/4, we can substitute these values into the point-slope form:
y - 2 = (-1/4)(x - 12).
Simplifying the equation:
y - 2 = (-1/4)x + 3,
y = (-1/4)x + 3 + 2,
y = (-1/4)x + 5.
Therefore, the equation that models Apple Street is y = (-1/4)x + 5.