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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: [tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]. To use this formula, you need two points and also, you need to assign these points to [tex] x_{1} [/tex], [tex] x_{2} [/tex], [tex] y_{1} [/tex], and [tex] y_{2} [/tex].
In this case, [tex] x_{1} [/tex] and [tex] x_{1} [/tex] is assigned to the ordered pair (1,3), while [tex] x_{2} [/tex] and [tex] y_{2} [/tex] is assigned to (3, 7). After assigning these points, you can substitute the pairs into the formula and simplify.
[tex] \frac{7-3}{3-1} =\frac{4}{2} = 2 [/tex]
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.
