If a line passes thru the points (-1,-1) and (2,3) find the slope of the line.?

Question

Give a point-slope equation for the line. Put the equation in slope-intercept form.

Answer 1

first find the slope of the line:
m = (y2-y1)/(x2-x1)
= (3-(-1))/(2-(-1))
= 4/3

next, use the point-slope form equation to get the equation of the line; you can use either point given:
y - y1 = m(x - x1)
y - 3 = (4/3) (x-2)
y - 3 = (4/3)x - 8/3

now put that in slope-intercept form:
y = (4/3)x - (8/3) + 3
y = (4/3)x - 17/3

Answer 2

Let's do one problem together, and then you can do the rest yourself. The point-slope form of an line is an equation of the form Y - Y1 = m (X - X1), where (X1, Y1) are any point on the line and m is the slope. This makes sense from the definition of slope, which is the rise over the run. It's saying, if you start at a point on the line, (X1,Y1) and go any distance away from it in the X direction, (X - X1), (we call that the run), you can find the rise, that is the corresponding distance in the y direction, by multiplying by the slope. Another way of seeing it: you can rewrite this form of the line equation as (Y - Y1)/(X - X1) = m, which is just the definition of the slope using the points (X, Y) and (X1, Y1) Anyway, enough theory. Your first two points are: (0,3),(-5,0). First, find the slope: m = (Y2 - Y1)/(X2 - X1) = (0 - 3)/(-5 - 0) = -3/-5 = 3/5 Then, just use either of the two points in the point slope form of the equation. Y - 3 = 3/5(X - 0) Y - 3 = 3/5(X) Now, the other questions can be solved using the point slope form of the equation too. Lines that are parallel have the same slope. This should be obvious from the definition of slope. They go up the same amount for the same amount over. Lines that are perpendicular have slopes that are the negative reciprocal of each other. Think of perpendicular lines as lines that have been rotated 90 degrees. Where one line goes in x, the other goes in y, and where one goes in y, the other goes in -x. So, for a line parallel to 4x-y=7 and passes through (2,-1), we first need to compute the slope of our given line. Rewriting the equation in point-slope form, we get 4x = y + 7 4(x - 0) = y + 7 Thus, the slope is 4. We want a line parallel to this, thus slope = 4, but passing through the point (2, -1). Using the point slope form of the equation, we get y - (-1) = 4(x - 2) y + 1 = 4(x - 2) The next one asks for the line perpendicular to 2x-7y=1 and passes thru (-4,0). Again, we first put it in point slope form to find the slope. 2x = 7y + 1 (2/7)x = y + 1/7 2/7(x - 0) = y - (-1/7). The slope is 2/7. The negative reciprocal of that is -7/2. Thus, we want the line with slope -7/2 that passes through (-4, 0) y - 0 = -7/2( x - (-4)) y = -7/2(x + 4) y = -7x/2 -14 Edit: Everyone, please note that y = mx + b is *not* the point slope form of an equation. That is the slope-*intercept* form of the equation. It is the same as the point slope form but only for the very specific point where x = 0. My answer is the only one which does what the homework specified, namely, find the point-slope form of the equation.

Answer 3

Just remember the simple formula for finding the slope:

y2-y1
_____

x2-x1

You already have the points, so just plug them in. Then once you have your slope (the m in y=mx +b) pig a pair of points (either pair will suffice.)

For instance, using point (2,3) the equation would look like this: 3=m(i.e. the slope that you found) * 2 + b

Then just solve for b and plug in your answers. Does that help? I'm not sure how to give the point-slope equation, but I'm sure you can find the formula online. Good luck.

Answer 4

point slope form is y-y1=m(x-x1)
since the points are (-1,-1) and (2,3) you need to graph those points. from (-1,-1) you go up 4 spaces to positive 3 and ovr 3 spaces to positive 2. the equation would now be as followed y-(-1)=4/3x-(-4/3)

i belive that is te right answer

Answer 5

This is easy.
Draw the line.
From (-1,-1) to (2,3) you go up 4 (positive), and over to the right 3 (positive). So, your slope is simply 4/3.

Answer 6

m=y2-y1 divided by x2-x1

m= (3--1) divided by (2--1)

m= 4/3

y=mx+c

y=4/3x+c

then sub in one of those points ((-1,-1) or (2,3)) to find the y-intercept

Good luck!

Answer 7

2- (-1) over 3- (-1) = 3/4

Answer 8

m = (3 + 1) / (2 + 1)
m = 4 / 3
y - 3 = (4/3)(x - 2)
y = (4/3).x - 8/3 + 9/3
y = (4/3).x + 1/3

Answer 9

Ummm all i remember is the intercept it -1 because (-1>-1<)

Answer 10

first of all graph it;
answer
y=4/7x+0
idk'that might not be the answer
i did it in my head