Rewrite the following equation in logarithmic form.
1 answer:
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Answer:
x + 3y = 30
Step-by-step explanation:
We are given that a line contains the points (12,6) and (-3,11).
We want to write the equation of this line in standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.
Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
So first, let's find the slope of the line.
The slope (m) can be found using the formula , where
and
are points.
Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.
Now substitute these values into the formula.
m=
m=
Subtract
m=
Simplify
m=
The slope is -1/3
Here is the equation of the line so far in slope-intercept form:
We need to solve for b.
As the equation passes through (12,6) and (-3,11), we can use either one to help solve for b.
Taking (12, 6) for example:
Multiply
Divide
6 = -4 + b
Add 4 to both sides.
10 = b
Substitute 10 as b in the equation.
Here is the equation in slope-intercept form, but remember, we want it in standard form.
In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.
Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.
So, let's multiply both sides by 3 to clear the fraction.
Multiply.
<u>x + 3y = 30</u>
<u></u>
Topic: finding the equation of the line (standard form)
See more: brainly.com/question/27575555
m = , y - 7 =
( x - 12), y =
x - 3
(a) calculate the slope using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂) = (12, 7)
m = =
=
(b) the equation of a line in point-slope form is
y - b = m(x - a )
where m is the slope and (a, b) a point on the line
using m = and (a , b) = (12, 7 )
y - 7 = (x - 12)
(c) the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange (b ) into this form
y - 7 = - 10
y = x - 3