SOLUTION: Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?

Question 225491: Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?
Found 2 solutions by drj, solver91311:
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?

Step 1. We'll put the equation of the line in slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Also we know that parallel lines have the same slope. So let's find the slope of the line passing through the point (6,-6) and (10,-4)

Given two points (x1,y1) and (x2,y2), then the slope m is given as

Step 2. Now we have to find the line with slope going through point (4,6).

Step 3. As mentioned earlier, given two points (x1,y1) and (x2,y2), then the slope m is given as

Step 4. Let (x1,y1)=(4,6) or x1=4 and y1=6. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:

Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.

Step 7. Add 6 to both sides of the equation

Step 7. ANSWER: The equation in slope-intercept form is where the slope and the y-intercept b=4.

Note: the above equation can be rewritten in standard form as

And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/-1 = -8.
Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
Slope is --1/2 = 0.5.
Equation in slope-intercept form: y=0.5*x+4.

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First determine the slope of the line that passes through (6,-6) and (10,-4) by using the slope formula:

where and are the coordinates of the given points.

Then use the fact that parallel lines have equal slopes, or

along with the other given point and the point-slope form of the equation of a line:

where are the coordinates of the given point and is the slope you calculated in the first step.

John

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