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What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = negative one-half(x – 4) y – 1 = one-half(x – 4) y − 1 = 2(x − 4)

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Therefore the equation for the the graphed line's parallel, which also passes through (4, 1), is y = -2*x + 9

What is equation?

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the formulas 3x + 5 and 14 make up the equation 3x + 5 = 14, with the word "equal" between them.

Here,

If two lines have the same slope, they are considered to be parallel.

This will allow us to determine the equation for the line that is perpendicular to the graphed line and goes through the points (4, 1): y = -2*x + 9.

Let's try to locate the line as follows:

Finding the graphed line's slope is the first step towards locating the line.

Keep in mind that a generic statement is anything like:

y = a*x + b

where a represents the slope and b the y-intercept

If the line does indeed travel through the points (x1, y1) and (x2, y2), then the slope of that line can be expressed as follows:

[tex]m=\frac{y_{2}- y_{1}}{x_{2} -x_{1} }[/tex]

As seen below, the graphed line crosses (-3, 3) and (-2, 1). The slope will therefore be:

[tex]m=\frac{1- 3}{2 -(-3) }[/tex]

Since the parallel line's slope is likewise 2, it will look somewhat like this:

y = -2*x + c

Using the knowledge that this line passes through, we may determine the value of c. (4, 1).

Thus, y = 1 must exist when x = 4.

When we swap these out in the line equation, we get:

-2*4 + c = 1

-8 + c = 1

1 + 8 = c = 9

Therefore the equation for the the graphed line's parallel, which also passes through (4, 1), is y = -2*x + 9

To know more about equation , visit

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