Questions: Find the slope-intercept equation that is parallel to y=5x+1 and passes through point (-2,3)

Transcript text: Find the slope-intercept equation that is parallel to $y=5 x+1$ and passes through point (-2,3)

Solution

Solution Steps

To find the slope-intercept equation of a line parallel to a given line, we use the same slope as the given line. The line $ y = 5x + 1 $ has a slope of 5. We then use the point-slope form of the equation, $ y - y_1 = m(x - x_1) $, where $ m $ is the slope and $(x_1, y_1)$ is the given point. Finally, we convert it to the slope-intercept form $ y = mx + b $.

Step 1: Identify the Slope

The given line is $ y = 5x + 1 $. The slope of this line is $ m = 5 $.

Step 2: Use the Point-Slope Form

We need a line parallel to the given line, so it will have the same slope $ m = 5 $. The line must pass through the point $(-2, 3)$. Using the point-slope form:

\[ y - y_1 = m(x - x_1) \]

Substitute $ m = 5 $, $ x_1 = -2 $, and $ y_1 = 3 $:

\[ y - 3 = 5(x + 2) \]

Step 3: Convert to Slope-Intercept Form

Expand and simplify the equation:

\[ y - 3 = 5x + 10 \]

Add 3 to both sides:

\[ y = 5x + 13 \]