When given the slope and a point on the line, instead of the slope and y-intercept, the process of finding the equation of the line involves using the point-slope form of a linear equation. Here's how you would proceed:

1. Recall the Point-Slope Form:

The point-slope form of a linear equation is given by:

$y - y_1 = m(x - x_1)$

where:

• $m$ is the slope of the line,
• $(x_1, y_1)$ is a point on the line.

2. Substitute the Given Values:

• Substitute the given slope $m$ into the equation.
• Substitute the coordinates of the given point $(x_1, y_1)$ into the equation.

3. Simplify the Equation:

• After substituting, simplify the equation to put it in either the slope-intercept form $y = mx + b$ or the standard form $Ax + By = C$, depending on the requirement.

Example:

Let's say you're given the slope $m = 3$ and a point on the line $(2, -5)$.

1. Start with the point-slope form: $y - (-5) = 3(x - 2)$ Simplifying: $y + 5 = 3x - 6$

2. To put it in slope-intercept form, solve for $y$: $y = 3x - 6 - 5$ $y = 3x - 11$

So, the equation of the line is $y = 3x - 11$.

Conclusion:

The key difference is that when you have the slope and a point, you use the point-slope form to first establish the equation, and then you can convert it into the slope-intercept form or any other desired form.

Would you like to explore any more details or have other questions?

Here are some related questions that might be helpful:

1. How do you convert an equation from point-slope form to standard form?
2. What is the significance of the point-slope form of a line?
3. How would you find the y-intercept after using the point-slope form?
4. Can you determine the equation of a line if only two points are given?
5. How would the equation change if the slope is zero?

Tip: Always double-check the point's coordinates and the slope when substituting them into the point-slope form to avoid any calculation errors.