Answer:
The equation of the line is:
[tex]y=2x-1[/tex]
Step-by-step explanation:
Given the points
Finding the slope between the points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-5\right),\:\left(x_2,\:y_2\right)=\left(1,\:1\right)[/tex]
[tex]m=\frac{1-\left(-5\right)}{1-\left(-2\right)}[/tex]
[tex]m=2[/tex]
We know the slope-intercept form of the line equation
[tex]y=mx+b[/tex]
where m is the slope and b is the slope-intercept form
substituting the value m=2 and the point (-2, -5) to find the b-intercept
[tex]y=mx+b[/tex]
-5 = 2(-2) + b
b = -5+4
b = -1
Now, substituting m=2 and b=-1 in the slope-intercept form to get the equation of a line
y=mx+b
y=2x+(-1)
y=2x-1
Thus, the equation of the line is:
[tex]y=2x-1[/tex]
