SOLUTION: Please help. For the points (3,-2) and (-5,-4) find: the slope between them and the equation of the line that passes through them

Question 201702: Please help.
For the points (3,-2) and (-5,-4) find:
the slope between them and the equation of the line that passes through them
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
For the points (3,-2) and (-5,-4) find:
the slope between them and the equation of the line that passes through them.
--------------------------------------
the slope of the line is given by the equation (y2-y1)/(x2-x1).
let (3,-2) = (x1,y1)
let (-5,-4) = (x2,y2)
x1 = 3
y1 = -2
x2 = -5
y2 = -4
(y2-y1) = (-4) - (-2) = (-2)
(x2-x1) = (-5) - (3) = (-8)
(y2-y1)/(x2-x1) = (-2)/(-8) = (-1)/(-4) = (1/4)
your slope is (1/4).
equation for a line is y = m*x + b where:
m is the slope
b is the y-intercept (value of y when x = 0).
to find b, you take one of the points that you were given and substitute for y and x and solve.
take the point (x2,y2) which equals (-5,-4).
you have:
y = -4
x = -5
m = (1/4) which was calculated earlier.
substitute for x and y in the general equation of y = m*x + b to get
-4 = (1/4)*(-5) + b
multiply both sides of the equation by 4 to get:
-16 = (1) * (-5) + 4*b
which equals
-16 = -5 + 4*b
add 5 to both sides of the equation to get:
-11 = 4*b
divide both sides of the equation by 4 to get:
b = (-11/4)
you have m which is (1/4) and you have b which is (-11/4)
your equation is
y = (1/4)*x + (-11/4)
which becomes
y = (1/4)*x - (11/4)
a graph of this equation will look like this:

your y intercept is (-11/4) which is the same as (-2.75). this is found by taking the general equation and making y = 0 and solving.
your x intercept is 11 which you find by taking the general equation and making x = 0 and solving.
both your original points are on this line as you can see from the graph.
your slope is (1/4) which you can find easily by taking the y intercept and the x intercept and solving for the slope.
the y intercept is (0,-11/4)
the x intercept is (11,0).
x1 = 0
y1 = -11/4
x2 = 11
y2 = 0
y2 - y1 = 0 - (-11/4) = 11/4
x2 - x1 = 11 - 0 = 11
(y2-y1) / (x2-x1) = (11/4) / 11 = (1/4) / 1 = (1/4).
everything checks out.
your slope is (1/4)
your equation is y = (1/4)*x - (11/4).

RELATED QUESTIONS
Please help!!!! Find slope of line that passes through the points (2, -5) and... (answered by solver91311)

Please help me answer tis question, thanks(: FInd the slope-intercept form of the... (answered by ewatrrr)

Find the slope of the line that passes through the points (-3, -5) and (3,... (answered by smik)

HELP! :( Find the slope of a line that passes through the points (-2,1) and (3,... (answered by jim_thompson5910)

. Find the slope of the line that passes through the points (2, 3) and (5, 8). (answered by stanbon,harecurtis)

Find the slope of the line that passes through the points (2, 3) and (5, 8). (answered by jim_thompson5910)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by josmiceli)

Find the slope of the line that passes through points (-3,-4) and... (answered by Boreal,josgarithmetic)

. Find the equation, in slope-intercept form, of the line that passes through the points (answered by tutorcecilia)