Given the pts (-5,3)&(5,-3) Find the slope of the line. Write the equation for the line in the form ax+by+c=0?

Question

Given the pts (-5,3)&(5,-3) a.Find the slope of the line. b.Write the equation for the line in the form ax+by+c=0
c.Find the Y Intercept.

Answer 1

m = (y1 - y0) / (x1 - x0) = -3 - 3 / 5 - -5 = -6 / 10 = - 3 / 5
therefore, -3/5 is the slope. (answer to a.)

to find c, I would use y = mx + b and solve for b.

-3 = (-3/5)(5) + b
b = 0 therefore c = 0

in y = mx + b, the line is y = (-3/5)x. in y = ax + by + c form,
add to both sides.
y + (3/5)x = 0 then multiply everything by 5.
3x + 5y = 0 (answer to b.)

from before, we know that c = 0, so the y-intercept must be 0.

Answer 2

a. The slope of the line connecting the two points a=(-5,3) and b=(5,-3) is the just change in the "rise" over the "run" of the graph.

The rise is the difference (or change) in y-values, and the run is the difference/change in x-values.

The change in y is by minus ay, or -3 minus 3 = -6.
The change in x is bx minus ax, or 5 minus -5 = 10.
So the slope is -6/10 or -3/5.

You can also do it using the points in the reverse order:
The change in y is ay minus by, or 3 minus -3 = 6.
The change in x is ax minus bx, or -5 minus 5 = -10.
So the slope is 6/-10 or -3/5.

No matter what order you use, the slope will always come out to be the same - remember that important fact.
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b.Since we have a point, and a slope, we can write AN equation for the line in the following way (then we have to rearrange to get it in the form ax+by+c=0):
y-y1 = m*(x-x1), where (x1,y1) is a given point, and m is the slope.

In our case, let's use (-5,3) as (x1,y1) and m=-3/5 as we calculated above.

y-3 = (-3/5)*(x+5) [notice x - (-5) is x+5], and let's rearrange:
y-3 = (-3/5)x -3 [then add 3 to both sides]
y = (-3/5)x [multiply both sides by 5]
5y = -3x [add 3x to both sides]
3x+5y=0 [and that's your answer, where a=3, b=5, and c=0].

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c. The y-intercept is the point where the graph crosses the y axis. (or when x = 0).

Plug in x=0 into our equation:
3(0)+5y=0
So 5y=0
and y=0.
So the y-intercept is the point (0,0), or just 0 (the value of 0, the y-value where the graph crosses the axis).

Answer 3

The gradient is (y2 - y1)/(x2 - x1)
= (-3 - 3)/(5 - -5)
= -6/10
= -3/5

In the form y = mx + c:
m is the gradient
c is the y intercept.

You know the gradient from the first part (-3/5), so plug this in.

y = -3/5x + c

You also know a set of co-ordinates you can enter (-5, 3)

3 = (-3/5)(-5) + c
3 = -(-3) + c
3 = 3 + c
c = 0

So the y intercept is y = 0 i.e. (0,0) i.e. the origin

Your equation is now y = -3/5x

This can be rearranged

y = -3/5x
5y = -3x
3x + 5y = 0

Answer 4

you would first do upward push over run. upward push is the substitute in y and run is the substitute in x. to discover upward push, do y2-y1 (2-6) so the upward push is -4. The run is x2-x1 (3- -a million) so the run is 4 then do upward push over run = -4/4 = a million, so the slope is -a million next you want to discover the y intercept through. Slope intercept form is y=mx+b, so that you would plug in between the coordinates for x and y to discover b, the y intercept. m is the slope, a million shall we use (3,2) 2=-a million*3+b 2=-3+b upload 3 to both aspect b= 5 equation= -x+5=y Y=X-a million is the answer

Answer 5

Part a)
gradient ,m = (-3 - 3) / (5 - (-5)) = - 6/10 = - 3/5

Part b)
Line passes thro` (5, - 3)
Equation of line is given by:-
y - (-3) = (-3/5)(x - 5)
y + 3 = (-3/5)(x - 5)
5(y + 3) = -3(x - 5)
5y + 15 = -3x + 15
3x + 5y = 0

Part c)
Line passes thro` (0,0)