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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 . When we plug in our points, (2,6) and (5,0), we get  , or , or , 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, 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 , 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.