Answer:
[tex]y=x-1[/tex]
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 [tex](x_1, y_1)[/tex] and Slope [tex]m[/tex]
---> [tex]y-y_1=m(x-x_1)[/tex]
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 [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex], the slope is:
---> [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's use this formula for the points above:
[tex]4=x_1, 6=x_2, 3=y_1, 5=y_2[/tex]
[tex]\frac{5-3}{6-4} = \frac{2}{2} = 1[/tex]
Based on the above: Slope = 1 (or [tex]m=1[/tex])
3) Next, we use point slope form. Let's use coordinate pair (4, 3) -- It does not matter which one:
[tex]y-3=1(x-4)[/tex]
The 1 does not mean anything (since anything multiplied by 1 is itself, so it can be taken out:
[tex]y-3=x-4[/tex]
Now to get it to slope-intercept form ([tex]y=mx+b[/tex]) ---> We add 3 to both sides
---> [tex]y-3+3=x-4+3 \\ y=x-1[/tex]
y=x-1 is the final equation.
