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. (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Find the slope of the given line

First, we need to rewrite the equation \(x - 2y = 5\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
Starting with \(x - 2y=5\), we solve for \(y\):
Subtract \(x\) from both sides: \(- 2y=-x + 5\)
Divide each term by \(-2\): \(y=\frac{1}{2}x-\frac{5}{2}\)
The slope of the line \(x - 2y = 5\) is \(m=\frac{1}{2}\). Since parallel lines have the same slope, the slope of the line we want to find is also \(m = \frac{1}{2}\).

Step2: Use the point - slope form formula

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.
We are given the point \((-3,1)\), so \(x_1=-3\) and \(y_1 = 1\), and \(m=\frac{1}{2}\).
Substitute these values into the point - slope form formula:
\(y - 1=\frac{1}{2}(x-(-3))\)
Simplify the expression inside the parentheses: \(y - 1=\frac{1}{2}(x + 3)\)

Answer:

\(y - 1=\frac{1}{2}(x + 3)\)