Answer:
a) 13/10
b) [tex]y+15=\dfrac{13}{10}(x-5)[/tex]
c) [tex]y+2=\dfrac{13}{10}(x-15)[/tex]
d) Both equations are [tex]y=\dfrac{13}{10}x-\dfrac{43}{2}[/tex] so represent the same line
e) [tex]-\dfrac{43}{2}[/tex] °F ⇒ y-intercept
Step-by-step explanation:
a) Choose two ordered pairs from the table: (5, -15) and (15, -2)
Let [tex](x_1,y_1)[/tex] = (5, -15)
Let [tex](x_2,y_2)[/tex] = (15, -2)
Use the slope formula to find slope: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\implies m=\dfrac{-2+15}{15-5}=\dfrac{13}{10}[/tex]
b) Use point-slope with (5, -15)
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y+15=\dfrac{13}{10}(x-5)[/tex]
c) Use point-slope with (15, -2)
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y+2=\dfrac{13}{10}(x-15)[/tex]
d)
[tex]\implies y+15=\dfrac{13}{10}(x-5)[/tex]
[tex]\implies y=\dfrac{13}{10}x-\dfrac{43}{2}[/tex]
[tex]\implies y+2=\dfrac{13}{10}(x-15)[/tex]
[tex]\implies y=\dfrac{13}{10}x-\dfrac{43}{2}[/tex]
Therefore, they represent the same line
e) when x = 0:
[tex]y=\dfrac{13}{10}(0)-\dfrac{43}{2}=-\dfrac{43}{2}[/tex] °F
Represents the y-intercept on the graph
