There is a straight line passing through the x and y-axis having a y-intercept of 6. The triangle formed by this line and the x and y-axis has a shaded region area of 72 square units. Find the slope of this line.
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If you sketch the triangle, you will see that you have a right triangle with a height of 6 units. Area is 72 sq units, and we need to know the measurement of the base.
Area of a triangle = 1/2 *base * height or 1/2 * height * base, so...
72 = (1/2)(6) base
So base = 24 units.
We now know that every time the line drops six units, there is a run of 24 units. Slope is rise/run, so...
Slope = -6/24 or /1/4
(If you were tempted to omit the negative sign for the drop of six, you'd catch your error right away, since the sketch shows an obviously negatively sloped line.)
Area of a triangle = 1/2 *base * height or 1/2 * height * base, so...
72 = (1/2)(6) base
So base = 24 units.
We now know that every time the line drops six units, there is a run of 24 units. Slope is rise/run, so...
Slope = -6/24 or /1/4
(If you were tempted to omit the negative sign for the drop of six, you'd catch your error right away, since the sketch shows an obviously negatively sloped line.)