Question

Find the equation of a line passing through (-2/3, 5) that is parallel to 4x-2y=6. Express your answer in point-slope form.

Answer 1

Using the information given, it is found that the linear function is given by:

$y - 5 = 2\left(x + \frac{2}{3}\right)$

A linear equation, in point-slope formula, is modeled by:

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

In which:

• m is the slope.

• The point is $(x_1, y_1)$.

• If two lines are parallel, they have the same slope.

Parallel to 4x - 2y = 6, which, in standard form is:

$2y = 4x - 6$

$y = \frac{4}{2}x - \frac{6}{2}$

$y = 2x - 3$

Hence, the slope is $m = 3$.

Point $\left(-\frac{2}{3}, 5\right)$, hence, the equation of the line is:

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

$y - 5 = 2\left(x + \frac{2}{3}\right)$

To learn more about linear functions in point-slope form, you can take a look at brainly.com/question/13967935