Consider the line with equation
5x – 2y = 10.
(a) Find the y-intercept for the given line.
(b) Find the slope for a line parallel to the given line.
(c) Find the slope for a line perpendicular to the given line.
This is interesting, I got the first one correct for y = -5 because x = 0 but still do not get how you come up with 5/2 for the slope of the parallel line and the slope of the perpendicular one either? Can you please explain. Thanks!
(a) Find the y-intercept for the given line.
(b)Find the slope for a line parallel to the given line.
(c) Find the slope for a line perpendicular to the given line.
y intercept is when x = 0
-2y = 10
y = -5
2 y = 5 x - 10
y = (5/2) x = 5
so m, the slope, = (5/2)
m'= -1/m
m' = -2/5
how did you come up with (5/2)
To find the answers to these questions, we can use the equation of the line in slope-intercept form, which is written as y = mx + b, where m is the slope and b is the y-intercept.
(a) To find the y-intercept, we need to find the value of y when x is equal to 0. In other words, we set x = 0 in the equation and solve for y.
Given equation:
5x - 2y = 10
Setting x = 0:
5(0) - 2y = 10
-2y = 10
Dividing both sides by -2:
y = -5
Therefore, the y-intercept for the given line is -5.
(b) To find the slope for a line parallel to the given line, we need to use the fact that parallel lines have the same slope.
Given equation:
5x - 2y = 10
Rearranging the equation to be in the form y = mx + b:
-2y = -5x + 10
Dividing both sides by -2:
y = (5/2)x - 5
From this equation, we can see that the slope of the given line is 5/2. Therefore, any line parallel to the given line will also have a slope of 5/2.
(c) To find the slope for a line perpendicular to the given line, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The slope of the given line is 5/2. To find the negative reciprocal, we flip the fraction and change the sign.
Negative reciprocal of 5/2:
-2/5
Therefore, the slope for a line perpendicular to the given line is -2/5.