what equation in slope\intercept form represents the line that passes through the points (3,5) and (-9,2)

Question

what equation in slope\intercept form represents the line that passes through the points (3,5) and (-9,2)

Answer 1

To write the equation of a line, remember we always need a point and a slope. Here, we aren't given a slope, but we are given 2 points and we can find the slope from those 2 points.

First, let's find the slope. Let's let the first point, (3, 5) be (x₁, y₁) and the second point (-9, 2) be (x₂, y₂)

Recall: slope = m = (y₂ - y₁)/(x₂ - x₁)

So plugging in our values we get

m = (2 - 5)/(-9 - 3) = -3/-12 = 1/4

So our slope is 1/4.

Now, we can use the point-slope formula to find the equation of the line using the slope we found and either of the 2 points. I'll just use the 1st point, but you could use the 2nd instead if you prefer.

Point-slope formula:

y - y₁ = m(x - x₁)

y - 5 = 1/4(x - 3) --> now we just need to solve for y. Let's start by distributing 1/4(x - 3)

y - 5 = 1/4x - 3/4 --> Now let's add 5 to both sides.

y = 1/4x + 17/4 --> Remember, y = mx + b is slope-intercept form, so solving for y accomplishes this.

OR

y = .25x + 4.25