For this case we have that by definition, an equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points through which the line passes, then we find the slope:
[tex](x1, y1): (- 1, -5)\\(x2, y2): (- 3, -7)[/tex]
[tex]m = \frac {y2-y1} {x2-x1} = \frac {-7 - (- 5)} {- 3 - (- 1)} = \frac {-7 + 5} {- 3 + 1} = \frac {-2} {- 2} = 1[/tex]
Then, the equation is of the form:
[tex]y = x + b[/tex]
We substitute a point and find b:[tex]-5 = -1 + b\\-5 + 1 = b\\b = -4[/tex]
Finally we have:
y = x-4
Answer:
Option B
Answer: Option b)
[tex]y=x-4[/tex]
Step-by-step explanation:
The equation of a line in the intersecting slope form has the following form:
[tex]y=mx+b[/tex]
Where
m is the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points that belong to the line
[tex]b=y_1-mx_1[/tex]
In this case the points are: (–1, –5) and (–3, –7)
So:
[tex]m=\frac{-7-(-5)}{-3-(-1)}[/tex]
[tex]m=\frac{-7+5}{-3+1}[/tex]
[tex]m=\frac{-2}{-2}[/tex]
[tex]m=1[/tex]
Therefore
[tex]b=-5-1*(-1)[/tex]
[tex]b=-5+1[/tex]
[tex]b=-4[/tex]
Finally the equation of the line is:
[tex]y=x-4[/tex]
