Question

Which equation in slope-intercept form represents a line that passes through the point (2,3) and is

Answer 1

Answer:

The answer is below

Step-by-step explanation:

Which equation in slope-intercept form represents a line that passes through the point (2,3) and is perpendicular to the line y−9=23(x+7)

Solution:

The equation of a line in slope intercept form is given as y = mx + b, where m is the slope and b is the y intercept.

Given a line y−9=23(x+7)

y - 9 = 23x + 161

y = 23x  + 170. The slope of this line comparing with y = mx + b gives m = 23

Two lines are perpendicular if the product of their slope gives -1.

Let $m_1$ be the slope of the perpendicular line, hence:

$m_1(23)=-1\\\\m_1=\frac{-1}{23}$

Since the perpendicular line passes through (2, 3), we can get its equation using:

$y-y_1=m_1(x_x_1)\\\\y-3=\frac{-1}{23}(x-2)\\\\y= \frac{-1}{23}x+\frac{2}{23}+3\\\\ y= \frac{-1}{23}x+\frac{71}{23}$