If we plot all the points that satisfy the equation *y* = *mx* + *c*, we’ll see that we get a line with slope *m* and *y*-intercept *c*. This form of the equation of the line (we’ll see another next class) is called the *point-slope form* equation of a line.

Now that we’re familiar with this type of equation, we can find the equation of a line with a given slope that passes through a given point.

For example, if I want to find the equation of a line with slope –2 that passes through the point *A*(1, 2), we know the equation will have the form *y* = –2*x* + *c*, but we still need to find the *y*-intercept (in other words, we still need to find the value of *c*). Here we can use the fact that the point *A*(1, 2) should be on our line. Since *A* is on our line, we should have \[\begin{align}2&=-2(1)+c\quad \text{ and so}\\ 4&=c\end{align} \]

But this means we’ve just found the “right” value for *c*! Now we now know that the equation for the line with slope –2, and passing through *A*(1, 2), is *y* = –2*x* + 4. (You can check this using GeoGebra.)

Complete the questions below before our next class.

- Find the equation of the line with slope –1, passing through the point (1, 4).
- Find the equation of the line with slope –1, passing through the point (2, 0).
- Find the equation of the line that passes through (1, 3) and (2, –1).
- Find the equation of a line perpendicular to the line you found in question 3, which also passes through the point (1, 3).