Aim #49: How do we write the equation of a line in
point-slope form?
Name _____________________________
Date ____________
Unit 5 – Graphing
Math 8H
Aim #49 Classwork: Point-slope form of a line
1) a) On the graph provided, plot (3, 4) and draw a line through this point if the slope is 2.
b) Write the equation of this line in slope-intercept form
Since the slope is the same between any two points on a given line, it is possible to write the
equation of a line knowing only one point and the slope.
Consider the slope formula:
Let (x1, y1) be a given point on a line whose slope is m and let (x, y) be any other point on the
line.
With this information we can now rewrite the slope formula as:
Now, by cross multiplying, we get:
y - y1 = m(x - x1)
which is the point-slope form of the equation of a nonvertical line where (x1, y1) represents
a point on the line and m represents the slope of the line.
We now know two ways to write the equation of a line!
1)
2)
y - y1 = m(x - x1)
point-slope form
2) a) Write the equation of the line that passes through the point (3, 4) and
has a slope of 2 in point-slope form.
b) Rewrite your answer from part a in slope-intercept form showing this
is the same line found in question 1.
y - y1 = m(x - x1)
point-slope form
3) Write an equation in point-slope form for the line through the given point that has the given slope.
a) (3, -4); m = 6
b) (-8, 5); m =
c) (-7, -1); m =
y - y1 = m(x - x1)
point-slope form
4) Write an equation in point-slope form for the line that passes through the two given points.
a) (2, 7), (1, -4)
b) (-1, -5), (-7, -6)
c) (7, -3), (-1, 1)
y - y1 = m(x - x1)
point-slope form
5) Write an equation for the line that passes through (3, -5) and (-2, 1) in
point-slope form and slope-intercept form.
6) Consider the linear equation y + 4 = 3(x - 2)
a) Graph this line using the slope-intercept method.
b) Graph this line using the point-slope method.
Sum it up, Ms. C!
Point-slope form is another way of writing the equation of a line and has the form
______________________ where ______ is the point on the line
and ______ is the slope of the line.