Equation for a line that passes through (6,26) and has a slope of 3
Equation for a line that passes through the points (5,5) and (10,20)
Equation for a line that passes through (9,25) and has a slope of -3.
Equation for a line that passes through (1,) and is perpendicular to the line 4x+6y=18.
Equatuion for a cirle with a radius of 4 and a midpoint at (2,2).
I already know how to do these. Try them yourself first and show me where you got stuck.
The first three can all be done substituting in
y = m x + b
where m is the slope.
For the fourth one, put the equation in form y = m x + b first
Then find m' = -1/m
That is the slope of a line perpendicular to the original one
then do y = m'x + b and substitute in your point, which you forgot to type the y coordinate for.
In the last one a circle equation is of form
(x-k)^2 + (y-h)^2 = r^2
where (k,h) is the center and r is the radius.
y=mx+b
26=3(6)+b
b=26/18
b=13/9
To find the equation of a line that passes through a given point and has a given slope, you can use the point-slope form of a linear equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point, and m is the given slope.
1. Equation for a line that passes through (6, 26) and has a slope of 3:
Using the point-slope form, the equation is:
y - 26 = 3(x - 6)
2. Equation for a line that passes through the points (5, 5) and (10, 20):
First, calculate the slope using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 5) / (10 - 5) = 15 / 5 = 3
Now, choose one of the points and use the point-slope form:
Using (5, 5):
y - 5 = 3(x - 5)
3. Equation for a line that passes through (9, 25) and has a slope of -3:
Using the point-slope form:
y - 25 = -3(x - 9)
4. Equation for a line that passes through (1, ) and is perpendicular to the line 4x + 6y = 18:
First, find the slope of the given line. Rewrite it in slope-intercept form, y = mx + b:
6y = -4x + 18
Divide by 6:
y = (-4/6)x + 3/2
The slope of the line is -4/6, which simplifies to -2/3.
To find the perpendicular slope, take the negative reciprocal:
Perpendicular slope = -1 / (-2/3) = 3/2
Using the point-slope form with the point (1, ):
y - y₁ = m(x - x₁)
y - y₁ = (3/2)(x - x₁)
Substituting (1, ):
y - = (3/2)(x - 1)
5. Equation for a circle with a radius of 4 and a midpoint at (2, 2):
The general equation for a circle with a center at (h, k) and a radius r is:
(x - h)² + (y - k)² = r²
Substituting the given values, we have:
(x - 2)² + (y - 2)² = 4²
Simplify the equation as needed.