Question

A straight line passes through the origin and has a gradient of -2/3. Find its equation

Answer 1

First thing you have to realize is that the gradient is the slope of the line. Therefore, the problem is telling you that the slope of the line is -2/3. It passes through the point (0, 0). From there, you can write an equation in slope-intercept form, solving for the "b", which is the y-intercept. Either that or use the point-slope, which I find to be a bit more tedious.

Answer 2

The general form for a slope-intercept equation is y = mx + b. We have the slope of -2/3 which will go in for "m", and we also have the point (0, 0), which we can use for the x and the y in the general equation. It will be set up like this:
0 = -2/3(0) + b
and solve it for b.

Answer 3

From this we can see that b = 0, so the general form for the equation with a gradient of -2/3 passing through the origin is y = -2/3x

Answer 4

ohh thankyou ! there's another question i need help with- do you mind walking me through another question ?

Answer 5

Not at all!

Answer 6

For the following graph, find the equation of the line in the form y = mx + B, and then rewrite the equation in general form.

Answer 7

Ok, nice and easy. Really! ; )

Answer 8

Start with the "b", which is the y-intercept. The y-intercept exists where x = 0, or even easier to understand, where the line goes through the y-axis. Our line here goes through the y-axis at -2. So that's the 'b' in our equation.

Answer 9

So far we have y = mx - 2

Answer 10

Now we have to find the slope of the line. We can either use the formula or we can use the fact that slope is the rise over the run (the change in y over the change in x) to find the slope. In this case, let's use the formula, so you can see how it works. It will work every time to find a slope.

Answer 11

\[m=\frac{ y _{2}-y _{1} }{ x _{2} -x _{1}}\]

Answer 12

Our two coordinates, from the line are (0, -2) and (6, 0), right?

Answer 13

y_2 is 0 and y_1 is -2, x_2 is 6 and x_1 is 0, so fill them in:
\[m=\frac{ 0-(-2) }{ 6-0 }\]

Answer 14

\[m=\frac{ 0+2 }{ 6-0}=\frac{ 2 }{ 6 }=\frac{ 1 }{ 3 }\]

Answer 15

So the slope is 1/3. Now we can fill THAT in our equation to get
\[y=\frac{ 1 }{ 3 }x -2\]

Answer 16

And there you have it!

Answer 17

See how easy?!

Answer 18

thankyou so so so much !

Answer 19

You bet! Math is my first love!

Answer 20

An equation of a line can be found from

a. the slope and y-intercept <-------sub m and b into y = mx + b

b. the slope and one point on the line <-------sub m and ( x_0, y_0 ) into y - y_0 = m( x - x_0 )

c. any two points on the line. <-------use the two pionts to calculate m then sub either point into b.