Answer:
[tex]y = -4x + 5[/tex]
Step-by-step explanation:
We want to find the equation of the line that is perpendicular to:
[tex]\displaystyle y = \frac{1}{4} x - 5[/tex]
And which passes through the point (2, -3).
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
In other words, since the slope of the original line is 1/4, the slope of the perpendicular line will be -4.
We are also given that it passes through the point (2, -3). Hence, we can consider using the point-slope form:
[tex]\displaystyle y - y_1 = m(x- x_1)[/tex]
Substitute:
[tex]\displaystyle y - (-3) = -4 (x - (2))[/tex]
Simplify:
[tex]y + 3 = -4(x - 2)[/tex][tex]y = -4x + 5[/tex]
Distribute:
[tex]y + 3 = -4x +8[/tex]
And subtract:
[tex]y = -4x + 5[/tex]
In conclusion, our equation is:
[tex]y = -4x + 5[/tex]
