Answer:
Part 1) The slope is [tex]m=5[/tex]
Part 2) The slope is [tex]m=-2[/tex]
Part 3) The slope is [tex]m=2[/tex]
Step-by-step explanation:
Part 1) we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem we have
[tex]y=5x+1[/tex]
so
the slope is [tex]m=5[/tex]
Part 2) we know that
The equation of the line in standard form is equal to
[tex]Ax+By=C[/tex]
where
the slope is equal to [tex]m=-\frac{A}{B}[/tex]
in this problem we have
[tex]2x+y=6[/tex]
so
[tex]A=2,B=1,C=6[/tex]
substitute
[tex]m=-\frac{2}{1}[/tex]
[tex]m=-2[/tex]
Part 3) we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(2,3)\ B(5,9)[/tex]
Substitute the values
[tex]m=\frac{9-3}{5-2}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
