Question

For the system of equations shown below,
y=3x-4
y=2x+7, with the slopes being 3 and 2, how many solutions does this system have?

Answer 1

If two lines have different slopes, must they intersect or not?

Answer 2

no

Answer 3

What is the slope of a line?
Can you give an explanation using your own words?

Answer 4

the change in y over the change in x?

Answer 5

the slope of these are 3 and 2, so would they intersect on the y axis at 3 and 2?

Answer 6

No. Slope is not where they intersect the y-axis. That is the y-intercept, which is b in the equation
y = mx + b.

You are correct; slope is "the change in y over the change in x", but those are the words of your teacher or textbook.
What is your understanding of the meaning of slope of a line?

Answer 7

um, slope determines how far down or how high up a line is?

Answer 8

No.
I'll explain it.
Slope is a measure of the inclination of a line.
Inclination means tilt.

Answer 9

A line that tilts up to the right has a positive slope.
The higher the slope is, the steeper the slope.

Answer 10

ok, I'm following.

Answer 11

Look at the figure above.
A horizontal line has a slope of zero.
Any horizontal line, no matter where it crosses the y-axis, still has a slope of zero.
That is graph 1 in the figure above.

Answer 12

Now look at graphs 2, 3, and 4.
All lines tilt up to the right.
All have positive slopes.
The line that is steeper, has a larger number for the slope.
For example, starting from graph 4,
the 4th graph can have a slope of 6.
The third graph can have a slope of 1.
The 2nd graph can have a slope of 1/2.
Notice, 1/2, 1, and 6 are all positive numbers, but as the positive number gets larger, the line is steeper.

Answer 13

ok, i understand.

Answer 14

Now the same thing happens with negative slopes.