Question

Which equation represents the line that passes through the point (−2,2) and is parallel to y = 1 halfx + 8?

Answer 1

Y=mx+b
m=slope

pareaell lines have same slope

so if it is paralell to y=(1/2)x+8 ten the slope is 1/2
so
y=(1/2)x+b
find b
the point (-2,2)
x=-2 and y=2
sub
2=(1/2)(-2)+b
2=-1+b
3=b

y=(1/2)x+3 is the equation

Answer 2

The equation of the line is $\boxed{y = \frac{1}{2}x + 3}$ that passes through the point $\left( { - 2, 2} \right).$

Further explanation:

The linear equation with slope m and intercept $c$ is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}} \right) {\text{and} \left( {{x_2},{y_2}} \right)$ can be expressed as,

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

Given:

The passes through point is $\left( { - 2, 2} \right).$

The parallel line is $y = \dfrac{1}{2}x + 8.$

Explanation:

The passes through point is $\left( { - 2, 2} \right).$

The slope of the line $y = \dfrac{1}{2}x + 8$ is $\boxed{\frac{1}{2}}.$

If the lines are parallel to each other than slope of the lines are equal.

Substitute $\dfrac{1}{2}$ for $m$, $-2$ for $x$ and 2 for $y$ in equation $y = mx + c$ to obtain the value of $c$.

$\begin{aligned}2&= \frac{1}{2}\left( { - 2} \right) + c\\2&= - 1 + c\\2 + 1&= c\\3&= c\\\end{aligned}$

Substitute 3 for $c$ and $\dfrac{1}{2}$ for $m$ in equation $y = mx + c.$

$y = \dfrac{1}{2}x + 3$

The equation of the line is $\boxed{y = \frac{1}{2}x + 3}$ that passes through the point $\left( { - 2, - 2} \right).$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers, slope -6, passes (-2,-2), slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin, 1/2x+8, parallel.