Question

find an equation of the line containing the given pair of points. (1,4) and (3,5) y = (simplify your answer. type your answer in slope - intercept form. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Calculate the slope

Let $(x_1,y_1)=(1,4)$ and $(x_2,y_2)=(3,5)$. The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{5-4}{3-1}=\frac{1}{2}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{1}{2}$ and $(x,y)=(1,4)$.
$4=\frac{1}{2}(1)+b$
Solve for $b$: $b=4-\frac{1}{2}=\frac{7}{2}$

Step3: Write line equation

Substitute $m=\frac{1}{2}$ and $b=\frac{7}{2}$ into $y=mx+b$.
$y=\frac{1}{2}x+\frac{7}{2}$

Answer:

$y=\frac{1}{2}x+\frac{7}{2}$