Question

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

Answer 1

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: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. To use this formula, you need two points and also, you need to assign these points to $x_{1}$, $x_{2}$, $y_{1}$, and $y_{2}$.

In this case, $x_{1}$ and $x_{1}$ is assigned to the ordered pair (1,3), while $x_{2}$ and $y_{2}$ is assigned to (3, 7). After assigning these points, you can substitute the pairs into the formula and simplify.

$\frac{7-3}{3-1} =\frac{4}{2} = 2$

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.