Question

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 = (x – 4)
y – 1 = (x – 4)
y − 1 = 2(x − 4)

Answer 1

The slope of the line given is -2.

Since we need to find the parallel line we will use the same slope and the points given.

Parallel line: y - 1 = -2 (x - 4)

Hope this helps :)

Answer 2

The equation that is parallel to the given line and passes through the point (4, 1) in point-slope form is y - 1 = -2(x - 4)

The equation of the line passing through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given as:

$y - y_1 = m(x - x_1)$

where m represents the slope

Calculate the slope using the formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

For the line shown in the graph, the given points are:

(-3, 3) and (-2, 1)

The slope is calculated as:

$m = \frac{1-3}{-2-(-3)} \\m = -2$

The indicated point is (4, 1)

Substituting m = -2, x₁ = 4, and y₁ = 1 into the equation:

$y-y_1 = m(x - x_1)$

$y-1=-2(x-4)$

Therefore, the equation that is parallel to the given line and passes through the point (4, 1) in point-slope form is y - 1 = -2(x - 4)

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