Answer:
The equation of the line that contains the point (4,3) and is perpendicular to the line represented by the equation y=2/5x+3 will be:
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
Given the line
y=2/5x+3
comparing with the slope-intercept form of the line equation
Thus, the slope of the line is: m = 2/5
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 2/5
Thus, the slope of the the new perpendicular line = – 1/m = [-1]/[2/5] = -5/2
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the slope of perpendicular line m = -5/2 and the point (4, 3)
[tex]y-3=-\frac{5}{2}\left(x-4\right)[/tex]
Add 3 to both sides
[tex]y-3+3=-\frac{5}{2}\left(x-4\right)+3[/tex]
[tex]y=-\frac{5}{2}x+13[/tex]
Therefore, the equation of the line that contains the point (4,3) and is perpendicular to the line represented by the equation y=2/5x+3 will be:
