Graphing Linear Equations: math practice, Grade 8

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Math practice Grade 8 : Graphing Linear Equations — Zyro the alien explorer of Planète Maths

21 problems graded by difficulty (★ easy, ★★ medium, ★★★ hard). Try first, without looking at the solutions!

Sommaire

1 Read the slope and the y-intercept ★★★

For each equation, state the slope $m$ and the y-intercept $b$.

$y = 3x + 5$
$y = -2x + 7$
$y = \dfrac{x}{2} - 4$
$y = -x$

2 Complete a table of values ★★★

Complete the table for the equation $y = 2x - 3$.

$x$	$-1$	$0$	$1$	$2$	$3$
$y$	?	?	?	?	?

3 Is the point on the line? ★★★

The line is $y = x + 2$. Decide whether each point is on the line: $(3, 5)$, $(-2, 0)$, $(1, 4)$.

4 Slope from two points ★★★

Find the slope of the line through each pair of points.

$(1, 2)$ and $(4, 8)$
$(0, 5)$ and $(3, 2)$

5 True or false? ★★★

Say whether each statement is true or false, and explain.

The line $y = 4$ is horizontal.
The line $x = 4$ is horizontal.
The line $y = -3x + 1$ goes down from left to right.
The line $y = 5x + 1$ is less steep than the line $y = 0.5x + 1$.

6 Build an equation ★★★

Write the equation of each line in slope-intercept form.

Slope $-3$, y-intercept $2$.
Slope $4$, crossing the y-axis at $(0, -6)$.
Slope $0$, crossing the y-axis at $(0, 7)$.

7 Saving money ★★★

Maya has $15 in her piggy bank and adds $5 every week. Let $y$ be the amount in dollars after $x$ weeks.

Write an equation for $y$.
How much does she have after 6 weeks?
What do the numbers 5 and 15 mean in this model?

8 Graph a line from its equation ★★★

Consider $y = -2x + 3$.

Make a table of values for $x = -1, 0, 1, 2, 3$.
Explain how to graph the line using only the y-intercept and the slope.

9 Write the equation from the graph ★★★

The graph shows a line through the points A, C, and B.

Give the y-intercept.
Use A and B to find the slope.
Write the equation of the line.
Check your equation with point C.

10 From a table to an equation ★★★

The table shows a linear relationship.

$x$	$0$	$1$	$2$	$3$
$y$	$4$	$7$	$10$	$13$

Find the slope and the y-intercept.
Write the equation.
Predict $y$ when $x = 10$.

11 Linear or not? ★★★

Decide whether each table could come from a line. If it does, write the equation.

Table 1

$x$	$1$	$2$	$3$	$4$
$y$	$3$	$6$	$12$	$24$

Table 2

$x$	$0$	$2$	$4$	$6$
$y$	$10$	$6$	$2$	$-2$

12 Horizontal or vertical? ★★★

Consider the point $P(4, -3)$.

Write the equation of the horizontal line through $P$.
Write the equation of the vertical line through $P$.
Give the slope of each line.

13 Taxi fare ★★★

A taxi charges a flat fee of $3.50 plus $2.25 for each mile. Let $C$ be the total cost in dollars for $m$ miles.

Write an equation for $C$.
Find the cost of an 8-mile ride.
A passenger paid $30.50. How many miles did the ride cover?

14 A fractional slope ★★★

A line has slope $-\dfrac{1}{2}$ and y-intercept 5.

Write its equation.
Find $y$ when $x = 6$.
Describe how to plot three points of the line.

15 Two points, no intercept ★★★

A line passes through $(2, 7)$ and $(5, 16)$. Find its equation in slope-intercept form.

16 From standard form to slope-intercept form ★★★

Rewrite each equation as $y = mx + b$, then give its slope and y-intercept.

$2x + y = 6$
$3x + 4y = 12$

17 Parallel lines and common points ★★★

Look at the three lines: $y = 3x + 2$, $y = -3x + 2$, and $y = 3x - 5$.

Which two lines are parallel? Justify.
Which two lines cross the y-axis at the same point? Give that point.
Write the equation of the line parallel to $y = 3x + 2$ that passes through $(0, -4)$.

18 Draining a tank ★★★

A water tank holds 240 gallons. A pump removes 15 gallons every minute. Let $g$ be the number of gallons left after $t$ minutes.

Write an equation for $g$.
How much water remains after 10 minutes?
When is the tank empty?
What does the slope tell you? Convert 240 gallons to liters (1 gallon is about 3.785 liters).