Answer:
3) Option C [tex]y=-\frac{5}{3} x-11[/tex]
4) Option C[tex]y =\frac{3}{2} x-1[/tex]
Step-by-step explanation:
Question 3:
A line perpendicular to another line has a slope which is a negative reciprocal of the line which is perpendicular to it.
[tex]y=\frac{3}{5} x-1[/tex]
So the slope of its perpendicular line will be [tex]-\frac{5}{3}[/tex].
The standard slope intercept form of an equation of a line is [tex]y=mx+c[/tex].
[tex]4=-\frac{5}{3} (-9)+c\\c=-11[/tex]
Therefore, the equation of a line perpendicular to the given equation is [tex]y=-\frac{5}{3} x-11[/tex]
Question 4:
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope = \frac{8-5}{6-4} = \frac{3}{2}[/tex]
[tex]y=mx+c[/tex]
[tex]5=\frac{3}{2} (4)+c\\c=-1[/tex]
Therefore, the equation of a line passing through (4, 5) and (6, 8) is [tex]y =\frac{3}{2} x-1[/tex]
