OpenStudy (anonymous):

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?

3 years ago
OpenStudy (mathstudent55):

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

3 years ago
OpenStudy (anonymous):

no

3 years ago
OpenStudy (mathstudent55):

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

3 years ago
OpenStudy (anonymous):

the change in y over the change in x?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (mathstudent55):

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?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (mathstudent55):

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

3 years ago
OpenStudy (mathstudent55):

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

3 years ago
OpenStudy (mathstudent55):

|dw:1405051317845:dw|

3 years ago
OpenStudy (anonymous):

ok, I'm following.

3 years ago
OpenStudy (mathstudent55):

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.

3 years ago
OpenStudy (mathstudent55):

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.

3 years ago
OpenStudy (anonymous):

ok, i understand.

3 years ago
OpenStudy (mathstudent55):

Now the same thing happens with negative slopes.

3 years ago
OpenStudy (mathstudent55):

|dw:1405051850832:dw|

3 years ago