Problem 41 - Introductory Algebra for College Students

Question

Describe how to write the equation of a line if its slope and a point on the line are known.

Step-by-Step Solution

Answer

The equation of a line is written as \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. Substitute the given slope and point into the equation, then solve for \(c\). Finally, write the equation of the line with the found slope and y-intercept values.

Step 1: Remember the Slope-Intercept Equation

The equation of a line can be written in slope-intercept form. The formula for this is \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

Step 2: Substitute The Slope into the Equation

The given slope would be substituted for \(m\) in the equation. It will now look like: \(y = {slope}x + c\).

Step 3: Substitute The Known Point into the Equation

The known point is an ordered pair (x, y). These values are plugged into the equation and substituted for \(x\) and \(y\). This results in an equation that looks something like this: \({known\_y} = {slope}*{known\_x} + c\).

Step 4: Solve for the y-intercept

We now solve the equation from step 3 for \(c\) to get the y-intercept.

Step 5: Write the Equation of the Line

The final step is plugging \(m\) (the slope) and \(c\) (the y-intercept) back into the slope-intercept equation: \(y = {slope}x + {intercept}\). This is the equation of the line.