Write the equation of a line that is perpendicular to the line x = -5 and passes through the point (-3,-7)
x = -5 is a vertical line.
So, you want a horizontal line through (-3,-7)
Now, what might that be?
(-5,-7)????
(-3,-7), (-5,-7).
m = (-7-(-7))/(-5-(-3)) = 0/-2 = 0.
Y = mx + b = -7.
0*x + b = -7, b = -7,
Eq: Y = -7 = A horizontal line.
Or, just note that a horizontal line is expressed by the equation
y = k
for some k. Since we have the point (-3,-7), the line is just
y = -7
Right!
To find the equation of a line that is perpendicular to the line x = -5, we need to determine the slope of the original line. However, since x = -5 is a vertical line, it has an undefined slope.
In this case, a line that is perpendicular to the vertical line x = -5 will be a horizontal line. Horizontal lines have a slope of 0.
Given that the line passes through the point (-3,-7), we can determine the equation of the line using the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Substituting the given values, we have:
y - (-7) = 0(x - (-3))
y + 7 = 0(x + 3)
Simplifying, we have:
y + 7 = 0
y = -7
Therefore, the equation of the line that is perpendicular to x = -5 and passes through the point (-3,-7) is y = -7.