the point - slope form of the equation of the line that passes through (-9, -2) and (1, 3) is $y…

the point - slope form of the equation of the line that passes through (-9, -2) and (1, 3) is $y - 3=\frac{1}{2}(x - 1)$. what is the slope - intercept form of the equation for this line?\n$y=\frac{1}{2}x + 2$\n$y=\frac{1}{2}x-4$\n$y=\frac{1}{2}x+\frac{5}{2}$\n$y=\frac{1}{2}x-\frac{7}{2}$

the point - slope form of the equation of the line that passes through (-9, -2) and (1, 3) is $y - 3=\frac{1}{2}(x - 1)$. what is the slope - intercept form of the equation for this line?\n$y=\frac{1}{2}x + 2$\n$y=\frac{1}{2}x-4$\n$y=\frac{1}{2}x+\frac{5}{2}$\n$y=\frac{1}{2}x-\frac{7}{2}$

Answer

Explanation:

Step1: Expand the point - slope form

Start with $y - 3=\frac{1}{2}(x - 1)$. Distribute $\frac{1}{2}$ on the right - hand side: $y-3=\frac{1}{2}x-\frac{1}{2}$.

Step2: Isolate y

Add 3 to both sides of the equation. $y=\frac{1}{2}x-\frac{1}{2}+3$.

Step3: Simplify the constant term

Calculate $-\frac{1}{2}+3$. Since $3=\frac{6}{2}$, then $-\frac{1}{2}+\frac{6}{2}=\frac{-1 + 6}{2}=\frac{5}{2}$. So $y=\frac{1}{2}x+\frac{5}{2}$.

Answer:

C. $y=\frac{1}{2}x+\frac{5}{2}$