Write the equation of the line with the given slope and containing the given point.

[sucksatmath]

I'm just getting into the point slope section of my algebra class and I am having a hard time with the following equation. Plus I am extremely poor with fractions.

Write the equation of the line with the given slope and containing the given point.

m=4/5, (8,2)

If I use the slope formula:
y-y1=m (x-x1)
y-2=4/5(x-8)
y-2=4/5x-6 2/5
+2 +2
y=4/5x - 4 2/5

y=4/5x-22/5

Is this the right way? Thanks for any help.

 

[JeffM]

I'm just getting into the point slope section of my algebra class and I am having a hard time with the following equation. Plus I am extremely poor with fractions.

Write the equation of the line with the given slope and containing the given point.

m=4/5, (8,2)

If I use the slope formula:
y-y1=m (x-x1)
y-2=4/5(x-8)
y-2=4/5x-6 2/5
+2 +2
y=4/5x - 4 2/5

y=4/5x-22/5

Is this the right way? Thanks for any help.

You got the right answer, but there is a perhaps simpler way. If fractions bother you, apply what used to be denis's rule but now is Jeff's rule: eliminate fractions as much as possible.

\(\displaystyle (y - 2) = \frac{4}{5}(x - 8) \implies 5(y - 2) = 5 * \frac{4}{5}(x - 8) \implies 5y - 10 = 4(x - 8) = 4x - 32 \implies 5y = 4x - 22 \implies\)

\(\displaystyle y = \frac{4}{5}x - \frac{22}{5}.\)

Edit: By the way, it is a good habit to check your work. It will give you confidence and will save your bacon on tests.

\(\displaystyle x_2 = 0 \implies y_2 = \frac{4}{5}(0) - \frac{22}{5} = -\frac{22}{5}\ BUT\)

\(\displaystyle m = \dfrac{y_1 - y_2}{x_1 - x_2} = \dfrac{2 - \left(- \frac{22}{5}\right)}{8 - 0} = \dfrac{\frac{10}{5} + \frac{22}{5}}{8} = \dfrac{\frac{32}{5}}{8} = \dfrac{32}{5} * \dfrac{1}{8} = \dfrac{4}{5}.\)

 

[sucksatmath]

Awesome! Thats a great way to do it! I'm all about trying to remove the fractions! Thank you!