7.
The standard form: Ax + By = C
[tex]a)\ y=\dfrac{2}{3}x-5\qquad\text{add 5 to both sides}\\\\y+5=\dfrac{2}{3}x\qquad\text{subtract y from both sides}\\\\5=\dfrac{2}{3}x-y\qquad\text{multiply both sides by 3}\\\\15=2x-3y\\\\\boxed{2x-3y=15}[/tex]
[tex]b)\ \dfrac{4}{5}x-3y=10\qquad\text{myltiply both sides by 5}\\\\\boxed{4x-15y=50}[/tex]
[tex]c)\ y-5=\dfrac{1}{2}(x-10)\qquad\text{multiply both sides by 2}\\\\2y-10=1(x-10)\\\\2y-10=x-10\qquad\text{add 10 to both sides}\\\\2y=x\qquad\text{subtract 2y from both sides}\\\\0=x-2y\\\\\boxed{x-2y=0}[/tex]
8.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
a) We have the points (-4, 7) and (8, -9). Substitute:
[tex]m=\dfrac{-9-7}{8-(-4)}=\dfrac{-16}{12}=-\dfrac{4}{3}\\\\\boxed{slope=-\dfrac{4}{3}}[/tex]
b) We have the points (-2, 7) and (-2, 5). Substitute:
[tex]m=\dfrac{5-7}{-2-(-2)}=\dfrac{-2}{0}\ \boxed{!}[/tex] division by 0!
slope is undefined
9.
a) The equation of a horizontal line: y = a (a - any real number)
We have the point (-5, 8) → x = -5 and y = 8
Answer: y = 8
b) The equation of a vertical line: x = a (a - any real number)
We have the point (-3, -2) → x = -3 and y = -2
Answer: x = -3
