A city map is laid out on a coordinate plane. Elm Street is described by the line x + 2y = -6. Oak street intersects Elm Street at an right angle. Which of the following could be the equation for Oak Street?
a. 2x + y = 5
b. -2x + y = 3
c. x + 2y = 4
d. -x - 2y = 8
My answer: d?
see later post
To find the equation for Oak Street, we need to determine the slope of the line perpendicular to Elm Street. Since the line Oak Street intersects Elm Street at a right angle, it must have a negative reciprocal slope.
The given equation for Elm Street is x + 2y = -6, or rearranged in slope-intercept form, y = (-1/2)x - 3.
The negative reciprocal of -1/2 is 2. This means that the slope of Oak Street is 2.
Now, let's check each of the options to see which one has a slope of 2.
a. 2x + y = 5: The equation is not in slope-intercept form, so we need to rearrange it. y = -2x + 5. The slope of this line is -2, not 2. So, option a is not correct.
b. -2x + y = 3: Rearranging this equation gives y = 2x + 3. The slope of this line is 2, which matches the slope we need. So, option b could be the equation for Oak Street.
c. x + 2y = 4: Rearranging this equation gives y = (-1/2)x + 2. The slope of this line is -1/2, not 2. So, option c is not correct.
d. -x - 2y = 8: Rearranging this equation gives y = (-1/2)x - 4. The slope of this line is -1/2, not 2. So, option d is not correct.
Based on our analysis, the equation that could be the equation for Oak Street is option b: -2x + y = 3.