Question

the stairway to a cellar has a slope of -4/3, and the cellar is 2m below the ground. the equation y=-4/3x-2 models the stairway. Which graph represents this equation?

Answer 1

Shown below

Explanation:

The stairway to a cellar has a slope of -4/3, that is:

$m=-\frac{4}{3}$

On the other hand, the cellar is 2m below the ground. In other words:

$y-intercept: \\ \\ b=-2$

So this can be modeled by the equation of the line:

$y=-\frac{4}{3}x-2$

The line has a y-intercept at point (0, -2) and as x increases 3 units y decreases 4 units. So:

$x=3 \\ \\ y=-\frac{4}{3}(3)-2=-6 \\ \\ (3,-6) \ is \ also \ a \ point \ on \ the \ line$

Finally, let's draw a line that passes through:

$(0,-2) \ and \ (3,-6)$

By using graphing tool, we get the line shown below.

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