what is the equation, in point - slope form, of the line that is parallel to the given line and passes…

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)?\n○ y - 1=-2(x - 4)\n○ y - 1=-\frac{1}{2}(x - 4)\n○ y - 1=\frac{1}{2}(x - 4)\n○ y - 1=2(x - 4)

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)?\n○ y - 1=-2(x - 4)\n○ y - 1=-\frac{1}{2}(x - 4)\n○ y - 1=\frac{1}{2}(x - 4)\n○ y - 1=2(x - 4)

Answer

Answer:

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

Explanation:

Step1: Calculate the slope of the given line.

Use the points $(-3, 3)$ and $(-2, 1)$ from the graph. $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{-2 - (-3)} = \frac{-2}{-2 + 3} = \frac{-2}{1} = -2$$

Step2: Determine the slope of the parallel line.

Parallel lines have the same slope. The slope of the required line is $m = -2$.

Step3: Use the point-slope form.

The point-slope form is $y - y_1 = m(x - x_1)$. Use the slope $m = -2$ and the point $(4, 1)$. $$y - 1 = -2(x - 4)$$