Question

How to write the slope intercept form of the equation of the line through the given points?

Answer 1

Slope intercept form of an equation is:
y = mx + b
where m is the slope and b is the t intercept.

First you must determine the slope of the line. This is a ratio of how fast the line travels up or down vs how fast it is moving to the right. Another name for this is rise over run. The equation to find the slope is:
m = (y1 - y2) / (x1 - x2)

now to find b. We can plug in one of the points of the equation into our first equation along with the slope to get out b value.

So if our 2 points were (2, 3) and (3, 4) we could find slope intercept form like this:
m = (2 - 3) / (3 - 4)
m = -1 / -1
m = 1
Now taking point (2, 3)
3 = 1 * 2 + b
1 = b
Finally to plug our m and b into equation for answer:
y = 1x + 1
However, 1 * anything is redundant therefore:
y = x + 1