y = -1/5 x + 4 4/5
Explanation:
The given points: (3, -1) and (4, 4)
We apply the slope formula to get the slope. Then we insert into the equation of line.
slope = change in y/change in x
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ x_1=3,y_1=-1,x_2=4,y_2\text{ = }4 \end{gathered}[/tex]
slope = (4 -(-1))/(4-3) = (4+1)/(4-3)
slope = 5/1 = 5
The equation of line: y = mx + c
using any of the given points and m, we would get the intercept (c).
Using point (x, y): (3, -1)
-1 = 5(3) + c
-1 = 15 + c
c = -1-15
c = -16
The equation the line: y = 5x + (-15)
y = 5x - 15
For a line to be perpendicular to another, the slope of one must be equal to the negative reciprocal of the other.
First slope = 5
reciprocal of the slope = 1/5
negative reciprocal of the slope = -1/5
The point for the other line is (4, 4)
[tex]\begin{gathered} Point\text{ slope formula: }y-y_1=m\mleft(x-x_1\mright) \\ y-4\text{ = -1/5(x - 4)} \end{gathered}[/tex]
y -4 = -1/5 x + 4/5
y = -1/5 x + 4/5 + 4
y = -1/5 x + 4 4/5
Hence, the equation of the line that is perpendicular to the line shown on the coordinate grid is y = -1/5 x + 4 4/5
