Question 78913: How do I write the equation of the line that passes through point (-1,-2) with a slope of -7. Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given a line through the point (-1,-2) with a slope of -7. Write an equation for the line.
.
There are several ways that this can be done. One way is to use the equation:
.
.
in which m is the slope and the values of and come from the x and y
values of the point you were given. Substituting those values gives you the equation:
.
.
This simplifies to:
.
.
and that is one form of an equation for the line.
.
Another way you can do it is to use the slope-intercept form of an equation. The slope
intercept form is:
.
.
where m is the slope of the line and b is the value where the graph crosses the y axis.
In this case you were told that the slope was -7. So you can substitute that value for
m in the slope intercept form to get:
.
.
From the point you were given on the graph you know that the equation is true when
x = -1 and y = -2. Substitute those two values into the slope intercept form and you
get:
.
.
by doing the multiplication on the right side this equation becomes:
.
.
Subtract 7 from both sides and you have solved for b. When you do that subtraction
you get:
.
.
which simplifies to
.
Return to the slope intercept form we were working on:
.
.
and substitute -9 for b to get:
.
.
and this also is an equation for the graph you were given. Believe it or not, if you
take our first answer and manipulate it around, you can work it into this same answer of
.
.
Hope this helps you to understand a couple of ways to get the equation of a line when you
are given the slope of the line and a point on the line.
(