please help me with this problem? I have the answer but I need to know how to do it.
Write the slope intercept form the equations of the lines through the given point parallel to the given line and (B) perpendicular to given line.
point slope
((7,-2) m= 1/2
y=m x + b
YOu are given m, so parallel would be the same m, perpendicular would be -1/m
To solve for b, put in the x,y values, solve for b.
then y=slope*x+bUsolvedFor.
i still don't get how to do it
To write the slope-intercept form of the equation for a line, you need two pieces of information: the slope (m) and a point (x, y) that lies on the line. In this case, you are given the point (7, -2) and the slope m = 1/2.
To find the equation of a line through a given point parallel to a given line, you need to use the same slope as the given line.
The slope-intercept form equation is y = mx + b, where y is the dependent variable (usually the y-coordinate), x is the independent variable (usually the x-coordinate), m is the slope, and b is the y-intercept.
1. Parallel line:
Since the line you want to find is parallel to the given line, it will have the same slope of m = 1/2.
Using the point-slope form, you can substitute the values of m and the given point (7, -2) into the equation:
y - y1 = m(x - x1)
Where x1 and y1 are the coordinates of the given point.
y - (-2) = (1/2)(x - 7)
This equation simplifies to:
y + 2 = (1/2)(x - 7)
To convert this to the slope-intercept form, isolate y:
y + 2 = (1/2)x - (7/2)
y = (1/2)x - (7/2) - 2
y = (1/2)x - 7/2 - 4/2
y = (1/2)x - 11/2
So, the equation of the line through the point (7, -2) parallel to the given line is y = (1/2)x - 11/2.
2. Perpendicular line:
To find the equation of a line perpendicular to the given line, you need to find the negative reciprocal of the slope (m) of the given line. The negative reciprocal of 1/2 is -2.
Using the point-slope form with the given point (7, -2) and the negative reciprocal slope of m = -2:
y - y1 = m(x - x1)
y - (-2) = (-2)(x - 7)
Simplifying this equation gives you:
y + 2 = -2(x - 7)
y + 2 = -2x + 14
To convert this to the slope-intercept form, isolate y:
y = -2x + 14 - 2
y = -2x + 12
Therefore, the equation of the line through the point (7, -2) perpendicular to the given line is y = -2x + 12.
Now you have the slope-intercept form equations for the lines through the given point, both parallel and perpendicular to the given line.