Question

What is the equation of the line that passes through the points (4,3),(6,5)?

Answer 1

Answer:

In slope intercept form, the equation would be y = x - 1.

Step-by-step explanation:

Answer 2

Answer:

$y=x-1$

Skills needed: Point-slope Form

Step-by-step explanation:

1) First, let's try to make sense out of the problem. We are given two coordinate points and have to create a line out of it.

---> The most efficient way to solve this is with point-slope form.

The point slope form, given One coordinate point and Slope is:

Given coordinate pair  $(x_1, y_1)$ and Slope $m$

---> $y-y_1=m(x-x_1)$

2) Now, we have one coordinate pair/point, but we need slope.

---> The slope is the rate of change, and can be found with a formula:

Given two coordinate points $(x_1,y_1)$ and $(x_2, y_2)$, the slope is:

---> $\frac{y_2-y_1}{x_2-x_1}$

Let's use this formula for the points above:

$4=x_1, 6=x_2, 3=y_1, 5=y_2$

$\frac{5-3}{6-4} = \frac{2}{2} = 1$

Based on the above: Slope = 1 (or $m=1$)

3) Next, we use point slope form. Let's use coordinate pair (4, 3) -- It does not matter which one:

$y-3=1(x-4)$

The 1 does not mean anything (since anything multiplied by 1 is itself, so it can be taken out:

$y-3=x-4$

Now to get it to slope-intercept form ($y=mx+b$) ---> We add 3 to both sides

---> $y-3+3=x-4+3 \\ y=x-1$

y=x-1 is the final equation.