Answer:
Part 1) [tex]y=-\frac{1}{5}x-1[/tex]
Part 2) [tex]y=3x-16[/tex]
Part 3) [tex]y=4[/tex]
Step-by-step explanation:
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-intercept
Part 1) we have
(10,-3) (5,-2)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{-2+3}{5-10}[/tex]
[tex]m=\frac{1}{-5}[/tex]
[tex]m=-\frac{1}{5}[/tex]
Find the value of b
we have
[tex]m=-\frac{1}{5}[/tex]
[tex]point (10,-3)[/tex]
substitute in the equation [tex]y=mx+b[/tex] and solve for b
[tex]-3=-\frac{1}{5}(10)+b[/tex]
[tex]-3=-2+b[/tex]
[tex]b=-3+2=-1[/tex]
substitute
[tex]y=-\frac{1}{5}x-1[/tex]
Part 2) we have
(6,2) (7,5)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5-2}{7-6}[/tex]
[tex]m=\frac{3}{1}[/tex]
[tex]m=3[/tex]
Find the value of b
we have
[tex]m=3[/tex]
[tex]point (6,2)[/tex]
substitute in the equation [tex]y=mx+b[/tex] and solve for b
[tex]2=3(6)+b[/tex]
[tex]2=18+b[/tex]
[tex]b=2-18=-16[/tex]
substitute
[tex]y=3x-16[/tex]
Part 3) we have
(4,4) (-7,4)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{4-4}{-7-4}[/tex]
[tex]m=\frac{0}{-11}[/tex]
[tex]m=0[/tex]
This is a horizontal line (parallel to the x-axis)
The y-intercept b is equal to the y-coordinate
therefore
The equation of the line is
[tex]y=4[/tex]
