Question

a line has a slope of $\frac{1}{2}$ and passes through the point (8, 3). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m=\frac{1}{2}$ and the line passes through the point $(0,3)$.

Step2: Substitute values into the equation

Substitute $x = 0$, $y = 3$ and $m=\frac{1}{2}$ into $y=mx + b$. We get $3=\frac{1}{2}(0)+b$.

Step3: Solve for b

Simplifying the right - hand side of the equation $3=\frac{1}{2}(0)+b$, we have $b = 3$ since $\frac{1}{2}(0)=0$.

Step4: Write the equation of the line

Now that $m=\frac{1}{2}$ and $b = 3$, the equation of the line in slope - intercept form is $y=\frac{1}{2}x + 3$.

Answer:

$y=\frac{1}{2}x + 3$