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Graphing Linear Equations Quiz - CBSE Class 9 Mathematics

Free practice quiz: Graphing Linear Equations (CBSE Class 9 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 19 multiple-choice questions on Graphing Linear Equations, and 19 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Graph of a Linear Equation

A linear equation in two variables has infinitely many solutions (x, y).
Plotting all these solutions gives a straight line. Every point on the line is a solution.
The general form is ax + by + c = 0, where a and b are not both zero.

General form

\[ax + by + c = 0\]

Common mistake: Thinking a linear equation has only one solution. In two variables it has infinitely many, all lying on one straight line.

Slope-Intercept Form

In y = mx + c, m is the slope (steepness) and c is the y-intercept.
To find the slope from any equation, first make y the subject. Then read the coefficient of x.

Slope-intercept form

\[y = mx + c\]

Slope from general form

\[m = -\frac{a}{b}\]

Line through the origin

\[y = mx\]

Common mistake: Forgetting to divide every term by the coefficient of y. Or dropping the minus sign when moving the x-term across.

Slope from Points and Types

Slope = change in y divided by change in x between any two points on the line.
Positive slope rises left to right. Negative slope falls. Zero slope is horizontal.
y = k is a horizontal line with zero slope. x = k is a vertical line with undefined slope.

Slope through two points

\[m = \frac{y_2 - y_1}{x_2 - x_1}\]

Horizontal line

\[y = k\]

Vertical line

\[x = k\]

Common mistake: Subtracting in mismatched order, such as y_2 - y_1 over x_1 - x_2. This flips the sign of the slope.

Finding x- and y-Intercepts

The y-intercept is where the line cuts the y-axis. Put x = 0 and solve for y.
The x-intercept is where the line cuts the x-axis. Put y = 0 and solve for x.

x-intercept of ax + by + c = 0

\[x = -\frac{c}{a}\]

y-intercept of ax + by + c = 0

\[y = -\frac{c}{b}\]

Common mistake: Mixing up the intercepts. For the x-intercept you set y to zero, not x.

Parallel and Perpendicular Lines

Parallel lines have equal slopes but different y-intercepts.
Perpendicular lines have slopes whose product is minus one. Each slope is the negative reciprocal of the other.

Parallel

\[m_1 = m_2\]

Perpendicular

\[m_1 \cdot m_2 = -1\]

Common mistake: For a perpendicular line, taking only the reciprocal or only the negative. You must do both.

Exam tips

Always convert to y = mx + c first. Then slope and y-intercept can be read directly.
Check the sign of the slope with a quick sketch: rising means positive, falling means negative.
A line through the origin has zero intercept, so its equation is simply y = mx.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What does the graph of a linear equation represent?
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Answer: B. A straight line
A linear equation represents a straight line on the graph, showing a constant rate of change.
In the equation 2x + 4y = 8, what is the slope when rewritten in slope-intercept form?
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Answer: D. -0.5
To find the slope, rewrite the equation in the form of y = mx + b. This gives y = -0.5x + 2, with slope m = -0.5.
What is the equation of a line with slope 3 that passes through the origin?
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Answer: A. y = 3x
A line with slope 3 passing through the origin (0, 0) can be represented by the equation y = mx, hence y = 3x.
If the slope of a line is 0, what does that tell us about the line?
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Answer: B. It is horizontal
A slope of 0 indicates that the line does not rise or fall as it moves horizontally, hence it is a horizontal line.
What is the x-intercept of the line represented by the equation 2x + 3y = 6?
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Answer: B. 3
To find the x-intercept, set y to 0. The equation becomes 2x = 6, thus x = 3.