Question

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours, the velocity of the car is 54 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equation obtained in Part A for the first seven hours? (5 points)

Answer 1

Part A)

$\bf \begin{array}{ccllll} hours(x)&velocity(y)\\ -----&-----\\ 2&50\\ 6&54 \end{array}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 50}})\quad % (c,d) &({{ 6}}\quad ,&{{ 54}}) \end{array}$

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{54-50}{6-2}\implies \cfrac{4}{4}\implies 1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-50=1(x-2)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-50=x-2\implies \boxed{y-x=48}\impliedby \begin{array}{llll} standard\\ form \end{array}$

part B)

well, to graph a LINEar equation, since it's just a LINE, you simply need two points to graph a line, and since we know that y - x = 48.... if you want to know what's "y" when x = 7? or 7 hours, well

y - (7) = 48
y = 48 + 7
y = 55

so.. that's the point for the 7th hour, 7, 55, and you can pick any other point above, and graph it away.