find the slope of a line that passes through the following points. (4,5) and (3,0) using the perpendicular and parallel slopes write slope intercept form equations for both perpendicular and parallel lines all perpendicular lines pass through the point(2,5) and parallel lines (-3,2)
find the slope m of the line joining the two points.
All parallel lines have the same slope m
All perp. lines have slope -1/m
Check out the point-slope form of a line.
To find the slope of the line passing through the points (4,5) and (3,0), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's substitute the values:
slope = (0 - 5) / (3 - 4)
Simplifying, we get:
slope = -5 / -1
slope = 5
Therefore, the slope of the line passing through the points (4,5) and (3,0) is 5.
To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of the slope. The negative reciprocal of 5 is -1/5.
So, the slope of a perpendicular line is -1/5.
To find the slope of a line parallel to this line, we use the same slope of 5.
Now that we have the slopes, let's write the slope-intercept form equations for both the perpendicular and parallel lines.
Perpendicular line equation:
We know the line passes through the point (2,5), and the slope is -1/5. Let's use the point-slope form to write the equation:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 5 = -1/5(x - 2)
Simplifying further:
y - 5 = -1/5x + 2/5
Now, let's rearrange the equation to slope-intercept form (y = mx + b):
y = -1/5x + 2/5 + 5
Simplifying again:
y = -1/5x + 27/5
This is the equation of the perpendicular line.
Parallel line equation:
We know the line passes through the point (-3,2), and the slope is 5. Again, let's use the point-slope form to write the equation:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 2 = 5(x - (-3))
Simplifying:
y - 2 = 5(x + 3)
Now, let's rearrange the equation to slope-intercept form (y = mx + b):
y = 5x + 15 + 2
Simplifying further:
y = 5x + 17
This is the equation of the parallel line.