Formulas for Linear Equation Problems

Important Formulas of Linear Equation & key points to Remember

• Suppose, there are two linear equations: a₁x + b₁y = c₁ and a₂x + b₂y = c₂

Then,

(A) If \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}, then there will be one solution, and the graphs will have intersecting lines.

(B) If\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} =  \frac{c_{1}}{c_{2}}, then there will be numerous solutions, and the graphs will have coincident lines.

(C) If \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}≠ \frac{c_{1}}{c_{2}} then there will be no solution, and the graphs will have parallel lines.

Questions on Formulas of Linear Equation:

Question 1:

What is the slope-intercept form of the equation of a line?

a) $y=mx+b$

b) $y=mx-b$

c) $y=bx+m$

d) $y=bx-m$

Answer : (a)

Explanation:

The correct answer is (a). The slope-intercept form of a linear equation is $y=mx+b$, where $m$ represents the slope and $b$ represents the y-intercept.

Question 2:

Which form of a linear equation is useful when you know a specific point on the line and its slope?

a) Point-Slope Form

b) Slope-Intercept Form

c) Standard Form

d) None of the above

Answer: (a)

Explanation: The correct answer is (a). The point-slope form of a linear equation is written as y−y1​=m(x−x1​), where (1,1)(x1​,y1​) represents the coordinates of a point on the line, and $m$ is the slope.

Question 3:

What does the standard form of a linear equation look like? a) $y=mx+b$

b) $y=bx+m$

c) $Ax+By=C$

d) $Ax+By=D$

Explanation: The correct answer is (c). The standard form of a linear equation is $Ax+By=C$, where $A$ and $B$ are coefficients representing the coefficients of $x$ and $y$, respectively, and $C$ is a constant term.

Question 4:

Which of the following is the correct representation of the point-slope form of a linear equation?

a) $y=mx+b$

b) �−�1=�(�−�1)y−y1​=m(x−x1​)

c) $y=Ax+By$

d) y=m1​x+b

Explanation: The correct answer is (b). The point-slope form of a linear equation is represented as �−�1=�(�−�1)y−y1​=m(x−x1​), where (�1,�1)(x1​,y1​) represents the coordinates of a point on the line, and $m$ is the slope of the line. This form is useful when you know a specific point on the line and its slope.

Question 5:

How can you eliminate fractions from a linear equation?

a) Multiply both sides of the equation by a common denominator

b) Divide both sides of the equation by a common denominator

c) Add both sides of the equation by a common denominator

d) Subtract both sides of the equation by a common denominator

Explanation: The correct answer is (a). To eliminate fractions from a linear equation, multiply both sides of the equation by a common denominator. This process will clear the fractions and make the equation easier to solve.