Question

Can anyone help me out? I need the answer and can you explain it! I’ll make brainlist thanks!

Answer 1

Answer:

3) Equation of line is: 5x-8y+34=0

4) Equation of line is: 5x+y+5=0

Step-by-step explanation:

3) Equation of line parallel to $5x-8y+12=0$ and through point (-2,3)

When two lines are parallel they have same slope.

Converting the given equation $5x-8y+12=0$ to Slope intercept form i.e $y=mx+b$

$5x-8y+12=0\\-8y=-5x-12\\y=-\frac{5x}{-8}-\frac{12}{-8}\\y= \frac{5x}{8}+\frac{3}{2}$

Now comparing with $y=mx+b$ we get value of m i.e 5/8 which is slope of line.

Now, finding y-intercept using point (-2,3) and slope 5/8

$y=mx+b\\3=\frac{5}{8}(-2)+b\\3=-\frac{5}{4}+b\\b=3+\frac{5}{4}\\b=\frac{3*4+5}{4}\\b=\frac{12+5}{4}\\b=\frac{17}{4}$

So, y-intercept is b= 17/4

The required equation is:

$y=mx+b\\y=\frac{5x}{8}+\frac{17}{4}$

Writing in Standard form

$y=\frac{5x}{8}+\frac{17}{4}\\y=\frac{5x+17*2}{8} \\y=\frac{5x+34}{8} \\8y=5x+34\\5x-8y+34=0$

So, Equation of line is: 5x-8y+34=0

4) Equation of line perpendicular to $x-5y+2=0$ and through point (-2,5)

When two lines are perpendicular they have opposite slope i.e m=-1/m.

Converting the given equation $x-5y+2=0$  to Slope intercept form i.e $y=mx+b$

$x-5y+2=0\\-5y=-x-2\\y=-\frac{x}{-5}-\frac{2}{-5}\\y= \frac{x}{5}+\frac{2}{5}$

Now comparing with $y=mx+b$ we get value of m i.e 1/5 which is slope of given line.

Slope of required line will be: m=-1/m = -5

Now, finding y-intercept using point (-2,5) and slope -5

$y=mx+b\\5=-5(-2)+b\\5=10+b\\b=5-10\\b=-5$

So, y-intercept is b= -5

The required equation is:

$y=mx+b\\y=-5x-5$

Writing in Standard form

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

So, Equation of line is: 5x+y+5=0