Grade 9 Exam > Grade 9 Notes > Integrated Math 1 > Worksheet (with Solutions): Linear Equations & Graphs
Worksheet (with Solutions): Linear Equations & Graphs
# Linear Equations & Graphs Worksheet
Section A: Multiple Choice Questions
Q1: What is the slope of the line passing through the points (2, 3) and (5, 11)?
(a) \(\frac{8}{3}\)
(b) \(\frac{3}{8}\)
(c) 3
(d) 8
Q2: Which equation represents a line with a slope of -2 and a y-intercept of 5?
(a) \(y = 2x + 5\)
(b) \(y = -2x + 5\)
(c) \(y = -2x - 5\)
(d) \(y = 5x - 2\)
Q3: What is the x-intercept of the equation \(3x + 4y = 12\)?
(a) 3
(b) 4
(c) 12
(d) -3
Q4: Which of the following lines is parallel to \(y = \frac{1}{2}x + 3\)?
(a) \(y = \frac{1}{2}x - 7\)
(b) \(y = -2x + 3\)
(c) \(y = 2x + 3\)
(d) \(y = \frac{1}{3}x + 3\)
Q5: Solve for \(x\): \(5x - 7 = 18\)
(a) 5
(b) 2.2
(c) 11
(d) 25
Q6: What is the slope of a horizontal line?
(a) 0
(b) 1
(c) Undefined
(d) -1
Q7: Which point lies on the line \(2x - y = 8\)?
(a) (3, -2)
(b) (4, 0)
(c) (2, 4)
(d) (5, 3)
Q8: What is the solution to the equation \(\frac{x}{3} + 4 = 10\)?
(a) 2
(b) 6
(c) 18
(d) 42
Section B: Fill in the Blanks
Q9: The equation \(y = mx + b\) is called the __________ form of a linear equation.Q10: Two lines with slopes that are negative reciprocals of each other are called __________ lines.Q11: The point where a line crosses the y-axis is called the __________.Q12: A vertical line has a slope that is __________.Q13: The standard form of a linear equation is written as \(Ax + By = C\), where \(A\), \(B\), and \(C\) are __________.Q14: If a linear equation has the form \(y = 7\), the line is __________ and has a slope of 0.Section C: Word Problems
Q15: A taxi service charges a flat fee of $3.50 plus $0.75 per mile driven. Write an equation in slope-intercept form that represents the total cost \(C\) in dollars for \(m\) miles driven. Then find the total cost for a 12-mile trip.Q16: A water tank initially contains 80 gallons of water. Water drains from the tank at a rate of 5 gallons per minute. Write an equation that models the amount of water \(W\) (in gallons) remaining after \(t\) minutes. How much water remains after 10 minutes?Q17: A line passes through the points (-3, 4) and (6, -2). Find the slope of the line and write the equation in point-slope form using the point (-3, 4).Q18: Maria is saving money for a new bicycle. She currently has $85 and plans to save $15 each week. Write a linear equation representing her total savings \(S\) after \(w\) weeks. In how many weeks will she have at least $175?Q19: A cellular phone plan costs $25 per month plus $0.10 per text message sent. Another plan costs $40 per month with unlimited texting. Write equations for both plans and determine how many text messages make the two plans cost the same.Q20: The temperature in degrees Fahrenheit \(F\) is related to the temperature in degrees Celsius \(C\) by the equation \(F = \frac{9}{5}C + 32\). If the temperature is 25°C, what is the temperature in degrees Fahrenheit? Also, find the temperature in Celsius when it is 68°F.The document Worksheet (with Solutions): Linear Equations & Graphs is a part of the Grade 9 Course Integrated Math 1.
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Apr 26, 2026 Last updated
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