Question

write the slope - intercept form of the equation with the given point and slope. through (2,5) and m = 1/2. y = 1/2x + 4, y=-1/2x + 4, y = 4x - 1/2

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 are given $m=\frac{1}{2}$ and the point $(2,5)$.

Step2: Substitute values into the equation

Substitute $x = 2$, $y = 5$ and $m=\frac{1}{2}$ into $y=mx + b$. So, $5=\frac{1}{2}\times2 + b$.

Step3: Solve for $b$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times2=1$. Then the equation becomes $5 = 1 + b$. Subtract 1 from both sides to get $b=5 - 1=4$.

Step4: Write the final equation

Since $m=\frac{1}{2}$ and $b = 4$, the slope - intercept form of the line is $y=\frac{1}{2}x + 4$.

Answer:

$y=\frac{1}{2}x + 4$