Choose the equation below that represents the line passing through the point (1, -4) with a slope of 1/2.

Question

I need step by step help 

Answer 1

 

With using the formula y-y1/x-x1=m we can easily solve this problem. In this formula x, y changables and x1,y1 are the points that we know and m is slope. If we put the values in their places

y-(-4)/x-1=1/2

y+4=(x-1)/2

y=x/2-9/2 is the answer

Answer 2

Ask yourself what does the problem give you? It gives you 1 point and a slope, right? So, you answered your own question. You use the 1 point with the slope (point/slope) formula which is y-y1=m(x-x1).

You replace the y1 part with the y part of the point you were given. Then, replace the x1 part with the x part of the point. Look at the point they gave you: (1,-4)

The 1 is the x1 and the -4 is the y1. M= slope

So, replace your slope of m with 1/2

Then, just distribute:

y - (-4) = (1/2)(x -1)

y+4=1/2(x-1) combine the two negatives (-)*(-) = +

y + 4 = (1/2)x -1/2 Distributive property

y + 4 - 4 = (1/2)x - 1/2 -4 Subtract 4 from each side

y = (1/2)x -9/2 Simplify

Presto, you're done! ;)

Since the options show only part of the answer, you have to go up to the part that it shows and pick that one: y + 4 = 1/2 (x - 1)

Answer 3

So from your choices, the y+4 = 1/2(x-1) would be the correct answer

The point-slope formula say y₂ - y₁ = m (x₂ - x₁)

So you fill in your values of m = 1/2, x₁ = 1 and y₁ = -4

This results in y - -4 = 1/2(x-1)

y - -4 (two negatives make a positive) ==> y + 4

So you really have y + 4 = 1/2 (x - 1) ==> matches your third option

Answer 4

To find the equation of a line from a point and the slope, use the point-slope formula:

y - y₁ = m(x - x₁)

To use the formula, substitute the slope (1/2) for m, the x value of the coordinate (1) for x₁ and the y value of the coordinate (-4) for y₁

y - y₁ = m(x - x₁)                  Point-slope formula

y - (-4) = (1/2)(x -1)            Substitution

y + 4 = (1/2)x -1/2              Distributive property

y + 4 - 4 = (1/2)x - 1/2 -4    Subtract 4 from each side

y = (1/2)x -9/2                    Simplify