Answer:
k = 5.
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope, and b is the y-intercept(y when x = 0).
Perpendicular lines
When two lines are perpendicular, the multiplication of their slopes is -1.
Perpendicular to the line y=x−285.
This line has slope 1, so the line we want to find the equation has slope [tex]m = -1[/tex]
Then
[tex]y = -x + b[/tex]
Passes through (7, 0)
This means that when [tex]x = 7, y = 0[/tex]. So
[tex]y = -x + b[/tex]
[tex]0 = -7 + b[/tex]
[tex]b = 7[/tex]
So
[tex]y = -x + 7[/tex]
Find the value of k given that the line through (k, 2)
This means that when [tex]x = k, y = 2[/tex]. So
[tex]y = -x + 7[/tex]
[tex]2 = -k + 7[/tex]
[tex]k = 7 - 2 = 5[/tex]
The value of k is k = 5.
