Math Is Fun Forum

Monique

Member

Registered: 2007-02-17

Posts: 22

a poor desperate mother needing help again?

   need help to draw the graph of a line that passes through the point (-4, -2) and has a   gradient  of 2. dont know how to get the numbers to plot this graph?

and how would I find the point of the above line with the line y = -x + 2?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: a poor desperate mother needing help again?

I found this:
To calculate the grade of a section of highway, divide the rise (height increase) by the run (horizontal distance). This equation, used to calculate the ratio of rise-to-run for highway grades, is the same ratio as the slope "y/x" encountered in a Cartesian coordinate system. In the example above, the rise of the highway section is 100 feet, while the run is 1,000 feet. The resulting grade is thus 100 feet divided by 1,000 feet, or 0.1.

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The above is the same as slope or m in the equation y = mx + b, where m is the slope or grade.
Now the angle with a grade of 2 is 63.43494882 degrees, because the inverse tangent of 2 is
that 63.43 degree number.  And the tangent of 63.43494882 is 2 on my calculator.

So to draw the graph, put a point 4 left and 2 down from the origin and then get out a
protractor if it's okay to be just an estimate, and place it horizontally with the flat part
of the semi-circle horizontal and the center point on (-4,-2).
Now find 63 and a half degrees on the right side of the curve and make a dot on your paper.
This will be another point on the line, just connect the dots.
Hope that helps.

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igloo myrtilles fourmis

Monique

Member

Registered: 2007-02-17

Posts: 22

Re: a poor desperate mother needing help again?

Thanks but still very...

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: a poor desperate mother needing help again?

EDIT:   As Jane notes in the next post, I made a mistake.  Thanks Jane.  It's been edited now and hopefully is correct.   And hopefully corrected before you had a chance to read the flawed one which would have confused you further. 

The gradient, or slope, is the "rise over the run".   Plot the point that you know (-4, -2).   Now go up 2 on Y axis (the rise) and to the right 1 (the run).   That should take you to (-3, 0).   There is only one line which passes though any two points.   Draw that line and you have your graph.  To put your line in the y = mx + b format, you need to know 2 things:  the slope (m) which is 2, and the y-intercept (b).   The y intercept is where the line crosses the x axis, i.e. the value of y when x = 0.   You can look at the line you drew and see it passes through (0,6) so 0 is your y-intercept.  The equation of the line would then be y = 2x + 6.  (You could also figure out the y intercept by noting that from your original point of (-4,-2) you need to increase x by 4 to get to 0.   For every unit change in x (the rise), y increases by 2 since the slope is 2.  So y increase by 8 from -2 to +6).

If you're aksing where does this new line intersect with the line y = -x + 2, here's how to do that.   You have 2 equations that are equal to y so set those 2 equal to each other.
y = 2x + 6
y = -x + 2
2x + 6 = -x + 2
3x = -4
x = -4/3

Now plug that value of x into one of your original equations to get y.   
y = 2x + 6
y = 2(-4/3) + 6
y = -8/3 + 6
y = 10/3

To double check, plug your x and y values into the other equation.
y = -x + 2
10/3 = -(-4/3) + 2
10/3 = 10/3.

Looks right to me.

Last edited by pi man (2007-03-13 15:04:18)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: a poor desperate mother needing help again?

The equation I found was y = 2x + 6.

y = 2x would pass through the point (−2,−4), not (−4,−2).

Last edited by JaneFairfax (2007-03-13 13:59:01)

Monique

Member

Registered: 2007-02-17

Posts: 22

Re: a poor desperate mother needing help again?

Thankyou so much