Questions: Determine the equation of the line parallel to (y=2x+1) that goes through ((-5,3)). Sketch (y=2x+1) and the parallel line through ((-5,3)) found in part 1.

Transcript text: Determine the equation of the line parallel to $\boldsymbol{y}=2 x+1$ that goes through $(-5,3)$. Sketch $y=2 x+1$ and the parallel line through $(-5,3)$ found in part 1.

Solution

Solution Steps

Step 1: Identify the slope of the given line

The given line is $ y = 2x + 1 $. The slope-intercept form of a line is $ y = mx + b $, where $ m $ is the slope. Here, the slope $ m $ is 2.

Step 2: Use the point-slope form to find the equation of the parallel line

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. We have the point $(-5, 3)$ and the slope $ m = 2 $.

Substitute the values into the point-slope form: \[ y - 3 = 2(x + 5) \]

Step 3: Simplify the equation to slope-intercept form

Distribute and simplify the equation: \[ y - 3 = 2x + 10 \] \[ y = 2x + 13 \]