Question

use the given conditions to write an equation for the line in point - slope form and slope - intercept form. passing through (-3,1) and parallel to the line whose equation is x - 2y = 5. write an equation for the line in point - slope form. $y - 1=\frac{1}{2}(x + 3)$ (simplify your answer. use integers or fractions for any numbers in the equation.) write an equation for the line in slope - intercept form. (simplify your answer. use integers or fractions for any numbers in the equation.)

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 already know from the point - slope form \(y - 1=\frac{1}{2}(x + 3)\) that the slope \(m=\frac{1}{2}\).

Step2: Expand the point - slope form

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

Step3: Solve for y

Add 1 to both sides of the equation. Since \(1=\frac{2}{2}\), we have \(y=\frac{1}{2}x+\frac{3}{2}+\frac{2}{2}\). Combine the fractions: \(y=\frac{1}{2}x+\frac{3 + 2}{2}=\frac{1}{2}x+\frac{5}{2}\).

Answer:

\(y=\frac{1}{2}x+\frac{5}{2}\)