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 (-3, 1)?\n○ y - 1=-\frac{3}{2}(x + 3)\n○ y - 1=-\frac{2}{3}(x + 3)\n○ y - 1=\frac{2}{3}(x + 3)\n○ y - 1=\frac{3}{2}(x + 3)

what is the equation, in point - slope form, of the line that is parallel to the given line and passes through the point (-3, 1)?\n○ y - 1=-\frac{3}{2}(x + 3)\n○ y - 1=-\frac{2}{3}(x + 3)\n○ y - 1=\frac{2}{3}(x + 3)\n○ y - 1=\frac{3}{2}(x + 3)

Answer

Answer:

$y - 1 = \frac{3}{2}(x + 3)$

Explanation:

Step1: Find the slope of the given line.

Identify two points on the line from the graph, such as $(-2, -4)$ and $(2, 2)$. Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. $$m = \frac{2 - (-4)}{2 - (-2)} = \frac{2 + 4}{2 + 2} = \frac{6}{4} = \frac{3}{2}$$

Step2: Determine the slope of the parallel line.

Parallel lines have the same slope. Therefore, the slope of the required line is also $\frac{3}{2}$. $$m_{parallel} = m = \frac{3}{2}$$

Step3: Use the point-slope form.

The point-slope form of a line is $y - y_1 = m(x - x_1)$. The line passes through the point $(-3, 1)$, so $x_1 = -3$ and $y_1 = 1$. Substitute the slope $m = \frac{3}{2}$ and the point $(-3, 1)$ into the formula. $$y - 1 = \frac{3}{2}(x - (-3))$$

Step4: Simplify the equation.

Simplify the expression in the parentheses. $$y - 1 = \frac{3}{2}(x + 3)$$ This is the equation of the line in point-slope form. Comparing this with the options, the last option matches.