Maths-
General
Easy
Question
Convert the equation 5x + 4y = 12 into y = mx + c and find its y-intercept.
Hint:
The given equation is in the general form of equation of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form by rearranging the term. Further, compare the equation with the standard form to get the y-intercept.
The correct answer is: y-intercept = 3
Step by step solution:
The given equation of the line is
5x + 4y = 12
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c
Rewriting the given equation, we have
4y = 12 - 5x
Dividing by 4, we get
Simplifying, we get
This is the y = mx + c form of the equation.
Comparing the above equation with y = mx + c, we get
Thus, we get
y-intercept = 3
We need to convert this equation in the slope-intercept form of the line, which is
Rewriting the given equation, we have
Dividing by 4, we get
Simplifying, we get
This is the y = mx + c form of the equation.
Comparing the above equation with y = mx + c, we get
Thus, we get
We can find the slope and y-intercept directly from the general form of the equation too; slope = 
and y-intercept = 
, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula.
Related Questions to study
Maths-
What must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x
What must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x
Maths-General
Maths-
𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.
a. What segment lengths in the diagram are equal?
b. Is A on 𝐴𝑃?
𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.
a. What segment lengths in the diagram are equal?
b. Is A on 𝐴𝑃?
Maths-General
Maths-
Use the square of a binomial to find the value. 562
Use the square of a binomial to find the value. 562
Maths-General
Maths-
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive odd numbers is 1 less than a perfect square.
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive odd numbers is 1 less than a perfect square.
Maths-General
Maths-
Name the polynomial based on its degree and number of terms.
Name the polynomial based on its degree and number of terms.
Maths-General
Maths-
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
Maths-General
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.
Maths-
Determine the equation of the line that passes through 
Determine the equation of the line that passes through
Maths-General
Maths-
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive even numbers is 1 less than a perfect square
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive even numbers is 1 less than a perfect square
Maths-General
Maths-
Identify a linear polynomial.
Identify a linear polynomial.
Maths-General
Maths-
Find the value of x. Identify the theorem used to find the answer.
Find the value of x. Identify the theorem used to find the answer.
Maths-General
Maths-
identify a cubic polynomial.
identify a cubic polynomial.
Maths-General
Maths-
Find the value of 𝑚 & 𝑛 to make a true statement.
(𝑚𝑥 + 𝑛𝑦)2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
Find the value of 𝑚 & 𝑛 to make a true statement.
(𝑚𝑥 + 𝑛𝑦)2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
Maths-General
Maths-
37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
i)Which equation models the scoring in the final round and the outcome of the contest
A symbol (usually a letter) in algebra represents an unknown numerical value in an algebraic expression or an equation. A variable is a non-fixed quantity that can be changed. Variables are essential because they are a significant component of algebra.
¶ Different Types of Variables
¶Dependent Variables: The variables whose values are determined by another variable's quantity.
¶Unrelated Variables: The values of an independent variable in an algebraic equation are unaffected by changes. Suppose an algebraic equation has two variables, x and y, and each x value is related to any other y value. In that case, x is an independent variable, and y is a dependent variable.
37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
i)Which equation models the scoring in the final round and the outcome of the contest
Maths-General
A symbol (usually a letter) in algebra represents an unknown numerical value in an algebraic expression or an equation. A variable is a non-fixed quantity that can be changed. Variables are essential because they are a significant component of algebra.
¶ Different Types of Variables
¶Dependent Variables: The variables whose values are determined by another variable's quantity.
¶Unrelated Variables: The values of an independent variable in an algebraic equation are unaffected by changes. Suppose an algebraic equation has two variables, x and y, and each x value is related to any other y value. In that case, x is an independent variable, and y is a dependent variable.
Maths-
Find the value of x. Identify the theorem used to find the answer.
Find the value of x. Identify the theorem used to find the answer.
Maths-General
Maths-
Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.
Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.
Maths-General
