Respuesta :
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
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
The equation of the line is [tex]\boxed{y = \frac{1}{2}x + 3}[/tex] that passes through the point [tex]\left( { - 2, 2} \right).[/tex]
Further explanation:
The linear equation with slope m and intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right) {\text{and} \left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The passes through point is [tex]\left( { - 2, 2} \right).[/tex]
The parallel line is [tex]y = \dfrac{1}{2}x + 8.[/tex]
Explanation:
The passes through point is [tex]\left( { - 2, 2} \right).[/tex]
The slope of the line [tex]y = \dfrac{1}{2}x + 8[/tex] is [tex]\boxed{\frac{1}{2}}.[/tex]
If the lines are parallel to each other than slope of the lines are equal.
Substitute [tex]\dfrac{1}{2}[/tex] for [tex]m[/tex], [tex]-2[/tex] for [tex]x[/tex] and 2 for [tex]y[/tex] in equation [tex]y = mx + c[/tex] to obtain the value of [tex]c[/tex].
[tex]\begin{aligned}2&= \frac{1}{2}\left( { - 2} \right) + c\\2&= - 1 + c\\2 + 1&= c\\3&= c\\\end{aligned}[/tex]
Substitute 3 for [tex]c[/tex] and [tex]\dfrac{1}{2}[/tex] for [tex]m[/tex] in equation [tex]y = mx + c.[/tex]
[tex]y = \dfrac{1}{2}x + 3[/tex]
The equation of the line is [tex]\boxed{y = \frac{1}{2}x + 3}[/tex] that passes through the point [tex]\left( { - 2, - 2} \right).[/tex]
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://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.
