On a map of downtown, 12th street is perpendicular to Avenue J. The equation y=-4x+3 represents 12th street. What is the equation representing Avenue J if it passes through the point (8,16)?
slope of 12th street = -4
so slope of Ave J = 1/4
so now you have m and a point
new equation:
y = (1/4)x + b
but (8,16) lies on it
16 = (1/4)(8) + b
16 = 2 + b
b = 14
y = (1/4)x + 14
In my class the question would have been worded this way:
Find the equation of the perpendicular to y = -4x +3, which passes through (8,16)
To find the equation representing Avenue J, we need to determine the slope and the y-intercept of the line. Given that 12th street is perpendicular to Avenue J, its slope will be the negative reciprocal of the slope of 12th street.
The equation for 12th street, y = -4x + 3, is in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. From this equation, we can see that the slope of 12th street is -4.
To find the slope of Avenue J, we take the negative reciprocal of -4. The negative reciprocal of a number is found by flipping its sign and inverting it. So, the negative reciprocal of -4 is 1/4.
Now, we have the slope (1/4) and a point (8,16) on Avenue J. We can use the point-slope form of a linear equation to find the equation of Avenue J, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - 16 = (1/4)(x - 8)
Expanding and simplifying the equation, we get:
y - 16 = (1/4)x - 2
y = (1/4)x + 14
Therefore, the equation representing Avenue J is y = (1/4)x + 14.