Answer:
5 and 5b: y=-2x+10
5a: y-2=-2(x-6)
Step-by-step explanation:
We can use the mentioned data points to identify the slope. Time will always the x coordinate/axis, so gallons will be the y coordinate/axis. As you probably already know, slope is rise over run, so we can measure the change in y over the change in x, or we can do [tex]\frac{y-y_{1}}{x-x{1}}[/tex]. When we plug in our points, (2,6) and (5,0), we get [tex]\frac{6-0}{2-5}[/tex], or [tex]\frac{6}{-3}[/tex], or [tex]\frac{2}{-1}[/tex], or simply -2. So our slope is -2.
We can use our y-intercept (which is (0,10), as mentioned in the attached graph and table) to make the equation, in slope-intercept form, [tex]y=-2x+10[/tex] This can answer both question 5 and 5b. Remember that slope-intercept form is written using the format y=mx+b, where x any given x-coordinate, y is the corresponding y-coordinate, m is the slope and b is the y-intercept.
To put this equation in point-slope form, one must first remember that point-slope form is written in the format [tex]y-y_{1} = m(x-x_{1})[/tex], using the coordinates of any given coordinates on the same line, except for the y intercept. m also represents slope in this equation. So for this one, we can easily use (2,6). we can plug in these coordinates to get the equation y-2=-2(x-6).
Hope this helps.
Graph and table were created using Desmos dot com graphing calculator.
