Respuesta :
The equation of the line in slope-intercept form is:
[tex] y = mx + b
[/tex]
Where,
m: slope of the line
b: cutting point with the y axis.
For the slope of the line we have:
[tex] m=\frac{y2-y1}{x2-x1} [/tex]
Substituting values we have:
[tex] m=\frac{-4-8}{-6-4} [/tex]
Rewriting we have:
[tex] m=\frac{-12}{-10} [/tex]
[tex] m=\frac{6}{5} [/tex]
Then, we choose an ordered pair:
[tex] (xo, yo) = (4, 8)
[/tex]
Substituting values in the generic equation of the line we have:
[tex] y-yo = m (x-xo)
[/tex]
[tex] y-8 = \frac{6}{5} (x-4) [/tex]
Rewriting we have:
[tex] y = \frac{6}{5}x -\frac{24}{5} + 8 [/tex]
[tex] y = \frac{6}{5}x -\frac{24}{5} + \frac{40}{5} [/tex]
[tex] y = \frac{6}{5}x + \frac{16}{5} [/tex]
Answer:
The equation of the line in slope-intercept form is:
[tex] y = \frac{6}{5}x + \frac{16}{5} [/tex]
Answer:
y = [tex]\frac{6}{5} x + \frac{16}{5}[/tex]
Step-by-step explanation:
The slope-intercept form is y = mx + b, where "m" is the slope and 'b" is the y-intercept.
Given: G(-6, -4) and E(4, 8)
Now we can use these points G(-6, -4) and E(4, 8) and find the slope.
Slope (m) = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Here x1 = -6, y1 = -4, x2 = 4 and y2 = 8
Plug in these values in the above formula, we get
slope(m) = [tex]\frac{8 - (-4)}{4 -(-6)}[/tex]
= [tex]\frac{12}{10}[/tex]
Slope (m) = [tex]\frac{6}{5}[/tex]
Now we can use the formula (y - y1) = m(x - x1) and find the required equation.
We can plug in m value and (x1, y1) value and find the equation.
y - (-4) = 6/5(x - (-6))
y + 4 = 6/5(x + 6)
Using the distributive property a(b + c) = ab + ac, we get
y + 4 = 6/5 x + 36/5
y = 6/5 x + 36/5 - 4
y =6/5 x +([tex]\frac{(36 - 20)}{5}[/tex]
y = [tex]\frac{6}{5} x + \frac{16}{5}[/tex]
