Write the equation of a line in slope intercept form that passes through (4,2) and (-6,1)

Question

Write the equation of a line in slope intercept form that passes through (4,2) and (-6,1)

Answer 1

The first step is to find the slope, so we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Now plug in the values of those coordinates: ^{1 - 2} / _{-6 - 4}

That leaves us with ^-1/_-10. the negatives in the numerator and denominator cancel out, so that leaves us with ¹/₁₀.

You have a couple options from here to make the slope-intercept equation. One is to use the point-slope equation and convert from there:

y - y₁ = m(x - x₁)

y - 2 = ¹/₁₀(x - 4)

y - 2 = ¹/₁₀ x - ⁴/₁₀

y - 2 = ¹/₁₀ x - ²/₅

y = ¹/₁₀ x - ²/₅ + 2

y = ¹/₁₀ x +1 ³/₅

Another way is to use one of the points given, place it in the s-i formula and solve for b:

2 = 4/10 + b

2 = 2/5 + b

2 - ²/₅ = b

1 ³/₅ = b

Plug b-value into the equation and once again:

y = ¹/₁₀ x +1 ³/₅

Answer 2

(4,2) (-6,1) have line through them with slope = (2-1)/(4+6) = 1/10 = (y-2)/(x-4)

y-2 = (1/10)(x-4)

y = x/10 -4/10 +2

y = (1/10)x + 8/5 in slope intercept form, where slope = 1/10 and intercept = 8/5

or

y = 0.1x + 1.6

Answer 3

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

=(2-1)/(4+6)

=1/10

y-2=1/10 (x-4)

10y-20=x-4

10y= x+16

Answer 4

Start with two-point form

(y - 2) / (x - 4) = (1 - 2) / (-6 -1)