I need help with "write in equation in slope-intercept form for the line that is parallel to to the given line line and and that passes through the given point.
y=1/2x=5;(4,-3) How do you find a line that is perpendicular. Please and thank you! :)
Assuming a typo, and that you mean
y = 1/2 x + 5
the slope is 1/2. Now, using the point-slope form, we want the line
y+3 = 1/2 (x-4)
or
y = 1/2 x -5
A perpendicular line will have slope -1/(1/2) = -2.
use that as you will.
To find an equation in slope-intercept form for a line that is parallel or perpendicular to another given line and passes through a given point, you need to follow a few steps:
Step 1: Find the slope of the given line
In the equation y = (1/2)x + 5, the coefficient of x, which is 1/2, represents the slope. So the slope of the given line is 1/2.
Step 2: Determine the relationship between the slopes of parallel and perpendicular lines
For parallel lines, the slope will be the same. In this case, since you need a line parallel to the given line, the slope should also be 1/2.
However, for perpendicular lines, the slope relationship is different. The negative reciprocal of the given slope will be the slope of the perpendicular line. The negative reciprocal of 1/2 is -2.
Step 3: Use the point-slope form to find the equation
Now that you have the slope for the desired line and a given point (4, -3), you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
For a line parallel to the given line:
Using the point (4, -3) and the slope 1/2, the equation would be:
y - (-3) = (1/2)(x - 4)
y + 3 = (1/2)(x - 4)
For a line perpendicular to the given line:
Using the point (4, -3) and the slope -2, the equation would be:
y - (-3) = -2(x - 4)
y + 3 = -2(x - 4)
These equations are in slope-intercept form, where the coefficient of x is the slope, and the constant term is the y-intercept.