Find the slope between points (-4,0) and (-1,2)
2 answers:
You might be interested in
<h2>Answer:</h2>
(a) y = x -
(b) y = 2x + 3
<h2>Step-by-step explanation:</h2>
(a) The equation of a line given by points M(x₁, y₁) and N(x₂, y₂) is given by:
y - y₁ = m(x - x₁) -------------------(i)
Where;
m = = slope or gradient of the line ---------------(ii)
Given points on the triangle are:
A(2,5)
B(1,-2)
C(-5,1)
To find the equation of line BC, we use the formulas in equations (i) and (ii) where the points of the line are B(1,-2) and C(-5,1) and;
x₁ = 1
y₁ = -2
x₂ = -5
y₂ = 1
==> First get the gradient using equation (ii) as follows;
m = =
m =
m =
==> Now, use equation (i) to find the equation of the line as follows;
y - (-2) = (x - 1)
y + 2 = (x - 1)
<em>Multiply both sides by 2</em>
2(y+2) = -1 ( x - 1 )
2y + 4 = -x + 1
2y = -x + 1 - 4
2y = - x - 3
y = x -
Therefore, the equation of the line is y = x -
(b) To find the perpendicular line from A to BC, note that
i. two lines are perpendicular if they meet at 90°
ii. the general equation of a line could also be written as <em>y = mx + c</em> where m is the slope and c is the intercept.
iii. when one line has a slope of m, then a perpendicular line to that line will have a slope of
The equation of line BC is y = x -
.
This means that BC has a slope of
A perpendicular line from A to BC will have a slope of 2.
Now to get the equation of this perpendicular line from A(2, 5) to BC, we use the general equation of a line given in equation (i)
where;
m = 2
x₁ = 2
y₁ = 5
Substitute these values into equation (i)
y - 5 = 2(x - 2)
Solving by simplification gives;
y - 5 = 2x - 2
y = 2x + 3
Therefore, the equation of the perpendicular line is y = 2x + 3
Answer:
The surface area ratio of cylinder a to cylinder b is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
The scale factor is equal to the ratio of its corresponding sides
so
Let
z------> the scale factor
x------> surface area of cylinder a
y------> surface area of cylinder b
step 1
Find the scale factor
step 2
Find the ratio of the surface areas
we have
substitute