Answer:
Please check the explanation
Step-by-step explanation:
Given the points
Determining 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(-5,\:-7\right),\:\left(x_2,\:y_2\right)=\left(3,\:1\right)[/tex]
[tex]m=\frac{1-\left(-7\right)}{3-\left(-5\right)}[/tex]
[tex]m=1[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point [tex](-5,-7)[/tex] and the slope [tex]m = 1[/tex] in the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-7\right)=1\left(x-\left(-5\right)\right)\\[/tex]
Hence, the equation in the point-slope form will be:
[tex]y-\left(-7\right)=1\left(x-\left(-5\right)\right)[/tex]
Writing the equation in slope-intercept form
As the point-slope of the equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
Putting m = 1 and (3, 1) to determine the y-intercept
[tex]y = mx+b[/tex]
[tex]1 = 1 (3) + b[/tex]
[tex]1 = 3 + b[/tex]
[tex]b = -2[/tex]
so putting [tex]b=-2[/tex] and m = 1 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y = (1)x + (-2)[/tex]
Therefore, the equation in slope-intercept form is:
[tex]y = x -2[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
As we already know the equation in slope-intercept form
[tex]y = (1)x + (-2)[/tex]
so just simplify the equation to write in standard form
[tex]y = (1)x + (-2)[/tex]
[tex]y = x - 2[/tex]
[tex]y - x = -2[/tex]
