Respuesta :
Answer:
y = 8x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given line v with equation
y = 8x + 2 ← in slope- intercept form
with slope m = 8
• Parallel lines have equal slopes , then
y = 8x + c ← is the partial equation
to find c, substitute (- 1, - 2 ) for x and y in the partial equation
- 2 = 8(- 1) + c = - 8 + c ( add 8 to both sides )
6 = c
y = 8x + 6 ← equation of line w
Answer:
[tex] y = 8x + 6 [/tex]
Step-by-step explanation:
Lines that are parallel have the same slope. The equation of line v is [tex]y = 8x + 2[/tex], where the slope ([tex]m_v[/tex]) is 8 while comparing with y = mx + c.
Since line w is parallel to line v, it will also have a slope of 8. Now, we can use the point-slope form of a linear equation to find the equation of line w. The point-slope form is given by:
[tex] y - y_1 = m(x - x_1) [/tex]
where [tex](x_1, y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.
For line w, with a point [tex](-1, -2)[/tex] and a slope of 8, the equation becomes:
[tex] y - (-2) = 8(x - (-1)) [/tex]
Simplify this equation:
[tex] y + 2 = 8(x + 1) [/tex]
Distribute the 8:
[tex] y + 2 = 8x + 8 [/tex]
Now, isolate [tex]y[/tex]:
[tex] y = 8x + 8 - 2 [/tex]
Combine constants:
[tex] y = 8x + 6 [/tex]
So, the equation of line w in slope-intercept form is:
[tex]y = 8x + 6[/tex]
