Question

Find an equation of the line that (a) has the same y -intercept as the line y + 5x + 9 = 0 and (b) is parallel to the line - 3x + 4y = 3 .

Answer 1

Equation of required line is:

$y = \frac{3}{4}x-9$

Step-by-step explanation:

First of all we will convert both equations in slope-intercept form

$y + 5x + 9 = 0$

Subtracting 5x from both sides

$y+9 = 0-5x\\y+9 = -5x$

Subtracting 9 from both sides

$y+9-9 = -5x-9\\y = -5x-9$

The y-intercept is -9.

Other equation is:

$- 3x + 4y = 3$

Adding 3x on both sides

$-3x+3x+4y = 3x+3\\4y=3x+3$

Dividing both sides by 4

$\frac{4y}{4} = \frac{3x+3}{4}\\y = \frac{3}{4}x+\frac{3}{4}$

As the required line has y-ntercept of line y + 5x + 9 = 0

So,

b = -9

And

The line is parallel to second line, so the slopes of both will be equal

$m=\frac{3}{4}$

Slope-intercept form of line is:

$y=mx+b$

Putting values of b and m

$y = \frac{3}{4}x-9$

Keywords: Equation of line, Slope-intercept form

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