Question

Write an equation in standard form for the line that passes through (3,-1) and (-5,-3)

Answer 1

0 = x - 4y - 7

Explanation:

Moving from (-5, -3) to (3, -1), we see that x (the run) increases by 8 and y (the rise) incrases by 2. Thus, the slope of the line connecting these two points is m = rise / run = 2/8, or 1/4.

Use the slope-intercept form of the equation of a straight line first:

y = mx + b becomes -1 = (1/4)(3) + b, or (after multiplying all three terms

by 4) -4 = 3 + 4b. Then 4b = -7, and b = -7/4.

Then the desired equation is y = (1/4)x - 7/4, or

4y = x - 7, or

0 = x - 4y - 7. This is the desired equation in standard form.

Answer 2

y = 1/4x - 1.75

Explanation:

standard form is y = mx + b

to get m you need to calculate the slope between the given points

m= (y1-y2)/(x1-x2)

m = (-1 - (-3))/(3 - (-5)) = 2/8 = 1/4

now you need to find the constant b by plugging in one of your points

y = 1/4x + b

-1 = 1/4(3) + b

b = -1 - (3/4)

b = -7/4 or -1.75