Find the equation in slope intercept form of the line that passes through the point (8,-2)and is parallel to the line.

Question

1. Find the equation in slope intercept form of the line that passes through the point (8,-2)and is parallel to the line.

 

2.Find the equation of the slope intercept form of the line that passes throught the point (-6,5) and is perpendicular to the line.

Answer 1

Slope intercept form will look like y=mx+b where m is the slope and b is the y-intercept.

 

I assume that you are given a picture of a line or an equation for a line.  If you are starting with the picture you need to determine the equation using the point where the line intercepts the y-axis (this is your b) and the slope of the line, which is the change in y position divided by the change in x position sometimes referred to as "rise over run" (this is your m).  If you are starting with an equation make sure you simplify it until it is in slope intercept form (y=mx+b).

 

Now to find the equation of the new line parallel to the original line and intersecting the given point you will use the y=mx+b formula and solve for b.  The slope m will be the same as the original line and you will plug in the coordinates of the given point (x,y).  The equation for the unknown is b=y-mx.

 

Now to find the equation for the new line perpendicular to the original line and intersecting the given point you will follow the same steps except the slope m will be -1/m of the original line, known as the inverse or the negative reciprocal.  Example if the original slope is m=1/2 the slope of the perpendicular line will be m=-2.

 

Example solutions:

 

1) Given line y= 3x + 2

 

The line parallel to this line but intersecting the point (8,-2) is found by using y=mx+b and solving for b

m=3 ; x=8 ; y=-2

b=y-mx

b=(-2)-(3)(8)=-26

y=3x-26

 

2) Given line y=3x + 2

 

The line perpendicular to this line but intersecting the point (-6,5) is found by using y=mx+b, solving for the negative reciprocal of m, and then solving for b

-1/m=-1/3 ; x=-6 ; y=5

b=y-(-1/m)x

b=(5)-(-1/3)(-6) = 3

y=-1/3x+3