What is the standard form of an equation of the line passing through these pairs of points?  a. (-1, -7), (1,3) b. (-5,1),(0,-2) c(-3,-2),(4,5)

We are asked to restrict your questions to one qustion -- the method supplied can be applied to the other problems:

(a) Given the points (-1,-7) and (1,3) we are asked to find the equation of the line through the points.

To find the equation of a line we need a point and the slope. We have two points, so we need to find the slope.

The slope between two points `(x_1,y_1),(x_2,y_2)` is given by the formula `m=(y_2-y_1)/(x_2-x_1)` . In this case the slope is `m=(3-(-7))/(1-(-1))=10/2=5`

** Order doesn't matter -- you could also have used `m=(-7-3)/(-1-1)=(-10)/(-2)=5` **

With the slope we can proceed in a number of different ways.

i. We can use the point-slope formula. Given a point `(x_1,y_1)` and slope m, the equation is `y-y_1=m(x-x_1)` . In this case, using the point (1,3), we get `y-3=5(x-1)==>y=5x-2`

ii. We know the form of the line is y=mx+b. We know the slope and a particular point, (1,3), so we can substitute these values and solve for b. 3=5(1)+b ==> b=-2 so y=5x-2.

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The equation of the line in slope-intercept form is y=5x-2

The equation of the line in general form is 5x-y=2

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Some books differ on "standard" form -- hopefully you will know from the context.