through (4, 3) and parallel to the line whose equation is 4x + y = 5

Question

find the equation of the line with the properties given 

Answer 1

Hi Emily,

 

Parallel lines have the same slope.

For. ax + by = c, slope is m=-a/b

 

4x + y = 5

m = -4/1 = -4

 

You want a line with slope -4 through (4, 3)

 

slope intercept form: y = mx + b

m = slope, b = y-intercept

 

y = -4x + b

Use (x, y) = (4, 3) to find b

3 = -4(4) + b

3 = -16 + b

19 = b

 

The equation is:  y = -4x + 19

 

In standard from: 4x + y = 19

 

Questions?

Answer 2

It must have the same slope as the given line, since it is parallel.

 

m = -4/1 = -4

 

In point-slope form, the equation is

 

y - y₁ = m(x - x₁)

 

y₁ = 3

x₁ = 4

m = -4

 

y - 3 = - 4(x - 4)

 

You can express this in standard form or some other form, if you wish.

Answer 3

Hi Emily,

 

Not sure which "formulas" you have learned at this point. Parallel lines have the same slope. 

 

The slope of the given line is found by solving for y (slope-intercept form).

 

So, y = -4x + 5 tells you the slope of the line is m = -4.

 

Now how do you write the equation of a line through (4,3) with a slope of -4. One way is point slope formula.

 

y-y₁=m(x-x₁₎

 

So y - 3 = -4 (x - 4). Simplify and solve for y for slope intercept form. 

 

Standard form is also what might be asked for:

 

y - 3 = -4x + 16

4x + y = 19

 

Check it out here:

 

https://www.desmos.com/calculator/q0lqv54xcw