What is the slope of the line that passes through points (5,-8) and (3,-3), and is the line through (5,-8) and (3,-3) horizontal, vertical, or oblique?
(A.) To determine the slope of a line which passes through `(x_1,y_1)` and `(x_2, y_2)` , use the formula :
`m = (y_2-y_1)/(x_2-y_2)`
Let point1 be (3,-3) and point2 be (5,-8).
`m= (-8-(-3))/(5-3) = (-8+3)/(5-3)=-5/2`
Hence, slope of the line is -5/2.
(B.) Note that for a horizontal line, the slope is zero. Let's say, if we have points (2,3) and (7,3). The slope of this is:
`m = (3-3)/(7-2) = 0/7 = 0`
Since m is zero, the line passing through these points is a horizontal line.
Whereas, a vertical line has no slope. For example if we have points (5,1) and (5,4), the slope is:
`m = (4-1)/(5-5)=3/0`
In fraction, we could not have a zero as a denominator. Hence, m is undefined and the line passing through (5,1) and (5,4) is vertical.
And for an oblique line, the value of the slope m is any real numbers except zero.
Since the points (5,-8) and (3,-3) has a slope equal to -5/4, then, the line containing these points is oblique.
A.) To determine the slope of a line which passes through (5,-8)and (3,-3) you can use the formula
Let point1 be (3,-3) and point2 be (5,-8). Which will result in m=-5/2
Meaning the slope of the line is -5/2. Meaning for every two x it increases, it decreases by -5 ys.
B. The line is oblique, its neither vertical or horizontal.
This because horizontal lines have a slope of 0.
Vertical lines have no slope, splope is the chage in y/ change in x and here we have no change in x. So the slope is undefined.
In oblique lines, the value of the slope m is all real numbers except zero.