Respuesta :
(-9,-2) (1,3)
slope = (3 - (-2) / (1 - (-9) = 5/10 = 1/2
y - y1 = m(x - x1)
slope(m) = 1/2
(1,3)...x1 = 1 and y1 = 3
sub
y - 3 = 1/2(x - 1)
y - 3 = 1/2x - 1/2
y = 1/2x - 1/2 + 3
y = 1/2x - 1/2 + 6/2
y = 1/2x + 5/2 <=== slope intercept form
slope = (3 - (-2) / (1 - (-9) = 5/10 = 1/2
y - y1 = m(x - x1)
slope(m) = 1/2
(1,3)...x1 = 1 and y1 = 3
sub
y - 3 = 1/2(x - 1)
y - 3 = 1/2x - 1/2
y = 1/2x - 1/2 + 3
y = 1/2x - 1/2 + 6/2
y = 1/2x + 5/2 <=== slope intercept form
Answer: [tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex]
Step-by-step explanation:
Equation of a line passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Similarly, the equation of line passing through (-9, -2) and (1, 3) is given by :-
[tex](y-3)=\dfrac{3-(-2)}{1-(-9)}(x-1)[/tex]
[tex](y-3)=\dfrac{3+2}{1+9)}(x-1)[/tex]
[tex](y-3)=\dfrac{5}{10}(x-1)[/tex]
[tex](y-3)=\dfrac{1}{2}(x-1)[/tex]
[tex](y-3)=\dfrac{1}{2}x-\dfrac{1}{2}[/tex]
Add 3 both sides , we get
[tex]y=\dfrac{1}{2}x-\dfrac{1}{2}+3[/tex]
[tex]y=\dfrac{1}{2}x+\dfrac{(2)(3)-1}{2}[/tex]
[tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex]
Hence, he slope-intercept form of the equation for this line :
[tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex]