Answer:
Problem 23) [tex]y=3x+6[/tex]
Problem 24) [tex]y=-\frac{1}{3}x-5[/tex]
Step-by-step explanation:
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(0,2)\ B(3,1)[/tex]
Substitute the values
[tex]m=\frac{1-2}{3-0}[/tex]
[tex]m=-\frac{1}{3}[/tex]
step 2
Problem 23
we know that
If two lines are perpendicular then the product of its slopes is equal to minus 1
so
[tex]m1*m2=-1[/tex]
Find the slope of the line
we have
[tex]m1=-\frac{1}{3}[/tex]
substitute in the equation and solve for m2
[tex](-\frac{1}{3})*m2=-1[/tex]
[tex]m2=3[/tex]
with the slope m2 and the point [tex](0,6)[/tex] find the equation of the line
Remember that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=3[/tex]
[tex]b=6[/tex] -----> the given point is the y-intercept
substitute
[tex]y=3x+6[/tex]
step 3
Problem 24
we know that
If two lines are parallel, then its slopes are the same
so
with the slope m1 and the point [tex](0,-5)[/tex] find the equation of the line
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]b=-5[/tex] -----> the given point is the y-intercept
substitute
[tex]y=-\frac{1}{3}x-5[/tex]
