Questions: Use the point-slope formula to find an equation of the line passing through the point (4,-6) and having slope 3. Write your answer in slope-intercept form.

Use the point-slope formula to find an equation of the line passing through the point (4,-6) and having slope 3. Write your answer in slope-intercept form.

Transcript text: 16. Use the point-slope formula to find an equation of the line passing through the point $(4,-6)$ and having slope 3 . Write your answer in slopeintercept form.

Solution

Solution Steps

Step 1: Start with the slope-intercept form of a line equation

The general form of a line in slope-intercept form is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 2: Substitute the given slope into the equation

Given that the slope $m$ is 3, we substitute it into the equation, resulting in $y = 3x + b$.

Step 3: Use the given point to solve for $b$

Given a point ($4, -6)$ through which the line passes, we substitute $x_1 = 4$ and $y_1 = -6$ into the equation to solve for $b$. This gives us the equation $-6 = 3(4) + b$. Solving for $b$, we find $b = -6 - (3)(4) = -18$.

Step 4: Substitute the values of $m$ and $b$ back into the slope-intercept form equation

Substituting $m = 3$ and $b = -18$ back into the equation, we get the final equation of the line: $y = 3x - 18$.