Question

Find the line parallel to y = 7x+2
that includes the point (3, -1).

Answer 1

? = 7

Explanation:

The equation of the line parallel to another line will have the same slope. The given line y = 7x + 2 has a slope of 7.

To find the equation of the line that passes through the point (3, -1) and is parallel to the given line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

So, the equation of the line parallel to y = 7x + 2 and passing through the point (3, -1) is:

y - (-1) = 7(x - 3)

Simplifying this, we get:

y = 7x - 21 - 1

y = 7x - 22

So, the equation of the line is y = 7x - 22.

Given the form of the equation y + 1 = ?(x -3). We then know the answer is y + 1 = 7 (x - 3)

Answer 2

The line's equation is :

↬ y + 1 = 7(x - 3)

Solution:

If two lines are parallel then their slopes are equal.

The slope of
`\sf{y=7x+2}` is 7, so the slope of the line parallel to it is 7.

Now, we should plug the slope and the point into the point slope equation. See, we're even given a hint :

Remember : y - y₁ = m(x - x₁).

This hint tells us the point slope equation.

Where

• m = slope
• (x₁, y₁) is a point on the line

So I plugin :

`\bf{y-(-1)=7(x-3)}`

Simplify.

`\bf{y+1=7(x-3)}`

This is it, we don't have to simplify all the way to slope intercept.

Hence, the equation is y + 1 = 7(x - 3)