SOLUTION: Hi, I have a problem with figuring out a linear equation. The question asks me to plot the graph showing the point and slope specified in the equation. Then I must rewrite in slo

Algebra ->  Linear-equations -> SOLUTION: Hi, I have a problem with figuring out a linear equation. The question asks me to plot the graph showing the point and slope specified in the equation. Then I must rewrite in slo      Log On


   



Question 154494: Hi, I have a problem with figuring out a linear equation. The question asks me to plot the graph showing the point and slope specified in the equation. Then I must rewrite in slope-intercept form and standard form.
Here is the equation
y-3=2/5(x-2)
Please help me.
Thanks
Ryan

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, I have a problem with figuring out a linear equation. The question asks me to plot the graph showing the point and slope specified in the equation. Then I must rewrite in slope-intercept form and standard form.
Here is the equation
y-3=2%2F5%28x-2%29

You must learn the three forms of the equation of a line:

1. Point-slope form:

y-y%5B1%5D=m%28x-x%5B1%5D%29

where the point (x%5B1%5D,y%5B1%5D) is on the line,
and m represents the slope of the line.

----------------------------

2. Slope-intercept form:

y=mx%2Bb

where m is the slope of the line and (0,b)
are the coordinates of the y-intercept.

-----------------------------

3. Standard form:

Ax%2BBy=C

Where A, B, and C are whole numbers, and A is positive.
[Don't confuse the capital B with the small b in the slope-
intercept form.

-----------------------------

y-3=2%2F5%28x-2%29

Multiply both sides by 5 to clear of
fractions:

5%28y-3%29=5·2%2F5%28x-2%29

5%28y-3%29=cross%285%29·2%2Fcross%285%29%28x-2%29

5%28y-3%29=2%28x-2%29

5y-15=2x-4

-2x%2B5y=11

Multiply through by -1 to make the first 
coefficient positive:

2x-5y=-11

That is the standard form.

----------------------------

To get the slope-intercept form, solve
that for y:

2x-5y=-11
-5y=-2x-11
%28-5y%29%2F%28-5%29=%28%28-2%29%2F%28-5%29%29x-%2811%2F%28-5%29%29

y=2%2F5x%2B11%2F5

Edwin