3/6/17 Week 9 Monday mindstretchers: Slope from a table/ Intercepts
1) How would you explain the relationship between finding slope from a graph,
from 2 points, and from a table of points?
2) You’ve most often seen linear equations in the slope-intercept (y = mx + b) form.
But what if you had to graph a line given in another form, such as the standard form:
ax + by = c?
a. One approach would be to use algebra and convert the given equation into y = mx +
b form the way you’re used to. Then you could graph it however you like best.
b. Another approach would be to find the x- and y-intercepts of the equation in
standard form and graph those.
For an example of these 2 methods, see A quick overview of graphing lines pages 3-4.
Try out both approaches here for 2x + 3y = –12.
Convert to y = mx + b and then graph.
Find the x- and y-intercepts and graph.
D. Stark 2/10/2017
1
3/6/17 Week 9 Monday mindstretchers: Slope from a table/ Intercepts
KEY
1) How would you explain the relationship between finding slope from a graph,
from 2 points, and from a table of points?
Slope is the measure of the steepness of a line. In other words, it’s a measure of
how far up it goes for every unit across it goes.
When you count “rise over run” from a graph, you’re finding that ratio—the
vertical change over the horizontal change (how far up for every unit across).
𝒚𝟐 −𝒚𝟏
says the same thing. y2 – y1 gives you the vertical
𝒙𝟐 −𝒙𝟏
change, that is, how many hops up or down you go on a graph. x2 – x1 gives you
the horizontal change, that is, how many hops right or left you go on a graph.
The slope formula m =
A table of values typically gives the x-coordinates in the left column and the ycoordinates in the right column. Each row essentially expresses an ordered pair
for a single point. So whether you just pick 2 points from the table or find the
difference between each row of x’s and then the difference between each row of
y’s and then put the change in y over the change in x, you’re finding the same
ratio as with the other methods.
2) You’ve most often seen linear equations in the slope-intercept (y = mx + b) form.
But what if you had to graph a line given in another form, such as the standard form:
ax + by = c?
a. One approach would be to use algebra and convert the given equation into y = mx +
b form the way you’re used to. Then you could graph it however you like best.
b. Another approach would be to find the x- and y-intercepts of the equation in
standard form and graph those.
For an example of these 2 methods, see A quick overview of graphing lines pages 3-4.
Try out both approaches here for 2x + 3y = –12.
D. Stark 2/10/2017
2
Convert to y = mx + b and then graph.
2x + 3y = –12
2x + 3y = –12
3y = –12 – 2x
3y = – 2x – 12
Find the x- and y-intercepts and graph.
2x + 3y = –12
x
0
–6
y
–4
0
3y = – 2x – 12
y=
−𝟐𝒙
y=–
𝟑
𝟐
𝟑
–
𝟏𝟐
𝟑
𝒙–4
D. Stark 2/10/2017
3