Question

How do i solve this i do not get it.... Find the equation of the line that contains the point left parenthesis negative 3 comma negative 9 right parenthesis and is parallel to the line 3 x plus 4 y equals 7. Write the equation in​ slope-intercept form, if possible.

Answer 1

Answer:

$y = -\frac{3}{4}x - \frac{45}{4}$

Step-by-step explanation:

When ever you are asked to draw a line that goes through a given point you should use point slope formula or $y - y_{1} =m(x - x_{1})$. In this problem you are asked to go through point (-3, -9) while being parallel to 3x+4y = 7.

1. Start by converting 3x+4y = 7 into slope intercept form (y = mx + b). To do this you first need to move 3x to the other side of the equation: 4y = -3x + 7. Then divide by 4 to get y alone: $y = -\frac{3}{4} x + \frac{7}{4}$.
2. Next, start plugging the numbers into the point slope formula given above, where $y_{1}$ is -9, $x_{1}$ is -3, and $m$ is $-\frac{3}{4}$. Your equation should look like this when you're done: $y - (-9) = -\frac{3}{4}(x - (-3))$.
3. When you subtract a negative you add so your equation becomes: $y + 9 = -\frac{3}{4}(x+3)$.
4. You then need to distribute the $-\frac{3}{4}$ into the $(x+3)$ and you should end up with something like this: $y+9 = -\frac{3}{4}x - \frac{9}{4}$
5. Finally, subtract the 9 from the left side and you have your answer: $y = -\frac{3}{4}x - \frac{45}{4}$