How do you write an equation of a line through the the point (-5, -3) and is parallel to the line 7x+2y=5?

2 Answers
Jun 26, 2018

2y+ 7x= -41

Explanation:

Since they're parallel, this means that they have the same gradient. So start by finding the gradient of the line by using the line equation provided,

To do this, it as to be in the y=mx+c format.

So:

2y= 5- 7x

y= 52- 72x

The gradient is the co-efficient of x, which is 72.

So:

m= -72

Next step is finding the y-intercept (c). To do this we make use of the gradient and the point provided.

So you get:

-3 = (-72) x (-5) +c

Here, notice that I'm using ymx+c to find my answer. Where y= -3, x= -5 and m= -72.

Now, let's find c:

-3 = 352 +c

c= -412

Now, SUBSTITUTION TIME!

y= -72x- 412

Take 2 to the other side by multiplication:

2y= 7x- 41

Then:

2y+ 7x= -41

Jun 26, 2018

7x+2y=41

Explanation:

Parallel lines have equal slopes

the equation of a line in slope-intercept form is.

xy=mx+b

where m is the slope and b the y-intercept

rearrange 7x+2y=5 into this form

subtract 7x from both sides and divide by 2

2y=7x+5

y=72x+52in slope-intercept form

with slope m =72

y=72x+bis the partial equation

to find b substitute (5,3) into the partial equation

3=352+bb=62352=412

y=72x412in slope-intercept form

multiply through by 2

2y=7x41

7x+2y=41in standard form