The area of a square is 320 square feet. estimate the length of one side
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
Answer:
Question 6: 26 crowns plus 15 ribbons.
Question 7: 10 footballs plus 42 basketballs.
Step-by-step explanation:
Question 6 explanation: Since the expression is 22 crowns plus 13 ribbons plus 2 ribbons plus 4 crowns, you can think of the different items as variables in an equation. Picture crowns are the variable , and ribbons as the variable
, this will help you solve the equation in an easier way that allows you to comprehend each step better. The equation will now be
, in order to find how many
(crowns) and
(ribbons) you have, you need to combine like terms in the expression. In other words, add the terms with the variable
together, and add the terms with the variable
together. Simplified, the equation will be
. Since the variables
and
were used to represent crowns and ribbons respectively, that means the correct answer is 26 crowns plus 15 ribbons.
Question 7 explanation: You can use the same method as you did in question 6, think of footballs and basketballs as the variables and
respectively. The equation will be
=
. Since the variable
was used to represent footballs and the variable
was used to represent basketballs, that means the correct answer would be 10 footballs plus 42 basketballs.