Question

What is the equation in point-slope form for the line parallel to y=5x-4 that contains p(-6,1)

Answer 1

y - 1 = 5 ( x + 6 )

Explanation:

• We know that when two lines are parallel the slope of both lines is equal.

• The formula that we use to find an equation of a line is y = m x + c

Here,

m ⇒ slope

• Now let us take a look at the given equation which is already drawn.

y = 5x - 4 ← equation of the old line

Now it is clear to us that,

m ⇒ slope of the line ⇒ 5

c ⇒ y-intercept ⇒ -4

• Therefore, the slope of the new line also will be 5.

That is, m = 5

• The question asked us to write the equation in point-slope form.
• The formula to write the equation in the line in point-slope form is :

y - y₁ = m ( x - x₁ ).

• Here,

m = slope

• Also, we can use the given coordinates to write the equation in point-slope form

( -6 , 1 ) ⇔ ( x₁ , y₁ )

• So, to find the equation of the new line we can replace m, y₁ & x₁ with 5, 1 & -6 respectively.

Let us solve this now

y - y₁ = m ( x - x₁ )

y - 1 = 5 ( x - ( -6) )

y - 1 = 5 ( x + 6 )

• And now let us write the equation of the new line in point - slope form.

y - 1 = 5 ( x + 6 )

Answer 2

`\displaystyle{y-1=5(x+6)}`

Explanation:

A point-slope form is written in the equation of
`\displaystyle{y-y_1=m(x-x_1)}`. Where
`\displaystyle{(x_1,y_1)}` is a coordinate point and
`\displaystyle{m}` is slope.

The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:

`\displaystyle{y-y_1=5(x-x_1)}`

Next, we are also given the point p(-6,1). Substitute
`\displaystyle{x_1}` = -6 and
`\displaystyle{y_1}` = 1 in:

`\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}`

Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)