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 [tex]m_1[/tex] be the slope of the perpendicular line, hence:
[tex]m_1(23)=-1\\\\m_1=\frac{-1}{23}[/tex]
Since the perpendicular line passes through (2, 3), we can get its equation using:
[tex]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}[/tex]
