the given line passes through the points (0, -3) and (2, 3). what is the equation, in point - slope form, of…

the given line passes through the points (0, -3) and (2, 3). what is the equation, in point - slope form, of the line that is parallel to the given line and passes through the point (-1, -1)?\n○ y + 1=-3(x + 1)\n○ y + 1=-\frac{1}{3}(x + 1)\n○ y + 1=\frac{1}{3}(x + 1)\n○ y + 1=3(x + 1)

the given line passes through the points (0, -3) and (2, 3). what is the equation, in point - slope form, of the line that is parallel to the given line and passes through the point (-1, -1)?\n○ y + 1=-3(x + 1)\n○ y + 1=-\frac{1}{3}(x + 1)\n○ y + 1=\frac{1}{3}(x + 1)\n○ y + 1=3(x + 1)

Answer

Answer:

$y+1=3(x+1)$

Explanation:

Step1: Calculate the slope of the given line.

Use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with points $(0, -3)$ and $(2, 3)$. $$m = \frac{3 - (-3)}{2 - 0} = \frac{3 + 3}{2} = \frac{6}{2} = 3$$

Step2: Determine the slope of the parallel line.

Parallel lines have equal slopes. The slope of the required line is $m = 3$.

Step3: Apply the point-slope form.

Use the point-slope form $y - y_1 = m(x - x_1)$ with slope $m=3$ and point $(-1, -1)$. $$y - (-1) = 3(x - (-1))$$

Step4: Simplify the equation.

Simplify the equation obtained in Step 3. $$y + 1 = 3(x + 1)$$