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Chapter 3: Problem 41

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

Short Answer

Expert verified
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 by step solution

01

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.
02

Substitute The Slope into the Equation

The given slope would be substituted for \(m\) in the equation. It will now look like: \(y = {slope}x + c\).
03

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: \({known\_y} = {slope}*{known\_x} + c\).
04

Solve for the y-intercept

We now solve the equation from step 3 for \(c\) to get the y-intercept.
05

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.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ for the given ordered pairs \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\). \(\left(x_{1}, y_{1}\right)=(4,-2) ;\left(x_{2}, y_{2}\right)=(6,-4)\)

Graph equation. \(3 y=9\)

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=-3 x+2$$

Find the coefficients that must be placed in each shaded area so that the equation's graph will be a line with the specified intercepts. \(\square x+\square y=12 ; x\) -intercept \(=-2 ; y\) -intercept \(=4\)

write each sentence as a linear equation in two variables. Then graph the equation. The \(y\) -variable is 3 more than the \(x\) -variable.
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