01.05 what is the slope intercept form equation of the line that's passing through (1,3) and (3,7)

Hello!

To find the slope-intercept form equation of the line that passes through the two points is found by first, calculating the slope using the slope formula and substitution, and secondly, finding the y-intercept of the equation through substitution.

Remember, slope-intercept form is written as: y = mx + b, where m is the slope and b is the y-intercept.

1. Find the slope

The slope formula is: . To use this formula, you need two points and also, you need to assign these points to , , , and .

In this case, and is assigned to the ordered pair (1,3), while and is assigned to (3, 7). After assigning these points, you can substitute the pairs into the formula and simplify.

The slope of these two points is 2.

2. Find the y-intercept

To find the y-intercept, you substitute an ordered pair into the slope-intercept equation with the slope that was just calculated. We can use either ordered pair because it will result in the same y-intercept.

y = 2x + b (substitute)

3 = 2(1) + b (simplify)

3 = 2 + b (subtract 2 from both sides)

1 = b

The y-intercept of the two points is (0, 1).

With the necessary values to complete the equation, we can write the final equation.

The slope-intercept form equation of the line that passes through the points (1, 3) and (3, 7) is y = 2x + 1.