What is the slope of the line that passes through (3/5,-2)(-6,2/9)?
I don't even have a good guess at this one. Thanks.
To find the slope of a line passing through two points, (x₁, y₁) and (x₂, y₂), you can use the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's plug in the values from the given points:
Point 1: (3/5, -2)
Point 2: (-6, 2/9)
Using the formula, we can calculate the slope:
slope = ( (2/9) - (-2) ) / ( -6 - (3/5) )
To simplify the calculations, let's first convert 3/5 to its decimal equivalent:
3/5 = 0.6
Now let's substitute the values into the slope formula:
slope = ( (2/9) - (-2) ) / ( -6 - 0.6 )
= ( (2/9) + 2 ) / ( -6 - 0.6 )
= ( (2/9) + (18/9) ) / ( -6 - 0.6 )
= ( (20/9) ) / ( -6 - 0.6 )
= ( (20/9) ) / ( -6.6 )
To divide by a fraction, we multiply by its reciprocal:
slope = ( (20/9) ) * ( -6.6/1 )
= -20 * 6.6 / 9
= -132 / 9
Now we can simplify the fraction:
slope = -14.67
The slope of the line passing through the points (3/5, -2) and (-6, 2/9) is approximately -14.67.