Help with Parallel Lines to y-intercept

[grae1229]

I am trying to solve:

Find an equation of the line that satisfies the given conditions.
y-intercept 6, parallel to the line 4x + 5y + 6 = 0

y=_______________

So far I have attempted to solve by giving the y-intercept a point of (0, 6) and
simplifying the equation for the line

4x + 5y + 6 = 0
5y=-4x-6
y=-4/5x-6/5

I believe the slope to be 4/5

Using the formula y-y[1]=m(x-x[1])
y-6=4/5(x-0)
5y-30=4x
5y-4x-30=0

The answer I come up with is incorrect, but is -4x + 5y - 30 = 0 for the line.
Help with how to solve this and any related information would be appreciated. Thank you.

 

[masters]

I am trying to solve:

Find an equation of the line that satisfies the given conditions.
y-intercept 6, parallel to the line 4x + 5y + 6 = 0

y=_______________

So far I have attempted to solve by giving the y-intercept a point of (0, 6) and
simplifying the equation for the line

4x + 5y + 6 = 0
5y=-4x-6
y=-4/5x-6/5

I believe the slope to be 4/5

Using the formula y-y[1]=m(x-x[1])
y-6=4/5(x-0)
5y-30=4x
5y-4x-30=0

The answer I come up with is incorrect, but is -4x + 5y - 30 = 0 for the line.
Help with how to solve this and any related information would be appreciated. Thank you.

Hi grae1229,

You did ok until you stated the slope of \(\displaystyle 4x+5y+6=0\)

You got it down to \(\displaystyle y=-\frac{4}{5}x-\frac{6}{5}\) with a slope of \(\displaystyle -\frac{4}{5}\)

but then you said the slope was \(\displaystyle \frac{4}{5}\)

Now, using the correct slope, maybe you can come up with the correct equation.

 

[BigGlenntheHeavy]

\(\displaystyle 4x+5y+6 \ = \ 0 \ \implies \ y \ = \ \frac{-4x-6}{5}, \ hence \ m \ = \ -\frac{4}{5}.\)

\(\displaystyle Now, \ we \ have \ a \ point \ (0,6) \ and \ a \ slope \ (m \ = \ -\frac{4}{5}), \ ergo,\)

\(\displaystyle y-6 \ = \ -\frac{4}{5}(x-0), \ y \ = \ \ -\frac{4}{5}x+6, \ see \ graph.\)

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