# 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

**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

So:

**2y= 5- #7x#**

**y= #5/2#- #7/2##x#**

The gradient is the co-efficient of

So:

**m= - #7/2#**

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 = (-

Here, notice that I'm using ** #y-mx+c#** to find my answer. Where

**y= -3**,

**and**#x# = -5

**m= -**#7/2# .

Now, let's find **c**:

-3 =

**c= - #41/2#**

Now, **SUBSTITUTION TIME**!

**y= - #7/2##x#- #41/2#**

Take 2 to the other side by multiplication:

**2y= #-7x#- 41**

Then:

**2y+ #7x#= -41**

#### Explanation:

#• " Parallel lines have equal slopes"#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=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=-7/2x+5/2larrcolor(blue)"in slope-intercept form"#

#"with slope m "=-7/2#

#y=-7/2x+blarrcolor(blue)"is the partial equation"#

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

#-3=35/2+brArrb=-6/2-35/2=-41/2#

#y=-7/2x-41/2larrcolor(red)"in slope-intercept form"#

#"multiply through by 2"#

#2y=-7x-41#

#7x+2y=-41larrcolor(red)"in standard form"#