CTJan27 Online Year 7 - Ploting Linear Relations

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Ploting Linear Relations

1

2

3

For the linear equation $y = 2x + 3$, what is the value of $y$ when $x = -4$?

$11$

$-5$

$-11$

$5$
4

Given the equation $y = -3x - 1$, find the value of $y$ when $x = 2$.

$-7$

$-5$

$5$

$7$
5

What is the value of $y$ for the equation $y = 5 - x$ when $x = -3$?

$-2$

$8$

$2$

$-8$
6

Consider the equation $y = -4x + 9$. Which of the following coordinate pairs is a valid solution for this equation?

$(2, 1)$

$(0, 4)$

$(-1, 12)$

$(3, -2)$
7

A table of values is created for the equation $y = x - 7$. What is the missing value in the table below?

x y
-2 -9
0 ?
3 -4

$0$

$7$

$-7$

$-4$
8

The table below is for the equation $y = -4x + 2$. Find the missing value, $a$.

x y
-1 6
$a$ 10
2 -6

$-3$

$-2$

$3$

$2$
9

Which of the following points lies on the line with the equation $y = 2x - 5$?

$(3, 1)$

$(1, -2)$

$(-2, -8)$

$(4, 4)$
10

For the equation $y = x - 5 + 2 - 8 + 4$, what is the value of $y$ when $x = -3$?

$-4$

$-10$

$4$

$10$
11

If you substitute $x = -5$ into the equation $y = -5x$, what is the resulting value of $y$?

$25$

$0$

$-25$

$1$
12

Calculate the value of $y$ for the equation $y = 10 - 2x$ when $x = 7$.

$4$

$24$

$-24$

$-4$
13

A table of values for the equation $y = 3x + c$ contains the point $(2, 5)$. What is the value of $c$?

$11$

$-11$

$1$

$-1$
14

Which of the following points does NOT lie on the line represented by the equation $y = x + 6$?

$(0, 6)$

$(3, 9)$

$(-2, 4)$

$(-1, -5)$
15

Find the missing value, $b$, in the table for the equation $y = 1 - 4x$.

x y
-2 9
0 1
3 $b$

$-13$

$11$

$-11$

$13$
16

For the equation $y = \frac{x}{3} - 2$, for which value of $x$ is $y=0$?

$-6$

$3$

$6$

$-3$
17

Which equation matches the given table of values?

x y
-1 -5
0 -2
1 1

$y = x - 4$

$y = 3x - 2$

$y = 2x$

$y = -3x - 2$
18

For the linear equation $y = -2(x+3)$, find the value of $y$ when $x = 1$.

$-8$

$-4$

$-2$

$8$
19

For the equation $y = 6 - x$, a table of values is created for $x = \{-2, 0, 2\}$. What is the sum of the corresponding $y$ values?

$0$

$12$

$6$

$18$
20

An incomplete table for $y = -5 - 2x$ is shown. Find the value of $m$.

x y
-4 3
$m$ -9
1 -7

$-2$

$-7$

$7$

$2$
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Understanding Slope and Intercepts of Linear Graphs

Understanding Slope as Rise over Run

The slope of a line measures its steepness. It is often described as "rise over run".

  • Rise: This is the vertical change between two points on the line (how much it goes up or down).
  • Run: This is the horizontal change between the same two points (how much it goes left or right).

A positive slope means the line goes up from left to right. A negative slope means the line goes down from left to right.

Calculating the Slope from Two Points

If you know two points on a line, $(x_1, y_1)$ and $(x_2, y_2)$, you can calculate the slope (denoted by the letter m) using the formula:

$m = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1}$

Example: Let's find the slope of a line passing through the points $(-8, 3)$ and $(-2, -12)$.

  1. Identify your points: $(x_1, y_1) = (-8, 3)$ and $(x_2, y_2) = (-2, -12)$.
  2. Plug the values into the formula. This calculation involves adding and subtracting negative and positive integers. $m = \frac{-12 - 3}{-2 - (-8)}$
  3. Simplify the numerator and the denominator: $m = \frac{-15}{-2 + 8} = \frac{-15}{6}$
  4. Reduce the fraction to its simplest form: $m = -\frac{5}{2}$

So, the slope of the line is $-\frac{5}{2}$.

Identifying and Finding Intercepts

The intercepts are the points where a line crosses the axes of the coordinate plane.

  • x-intercept: The point where the line crosses the horizontal x-axis. At this point, the y-coordinate is always 0. It has the form $(x, 0)$.
  • y-intercept: The point where the line crosses the vertical y-axis. At this point, the x-coordinate is always 0. It has the form $(0, y)$.

Finding Intercepts from an Equation

To find the intercepts from a linear equation (like $Ax + By = C$):

  1. To find the y-intercept: Set $x=0$ in the equation and solve for $y$.
  2. To find the x-intercept: Set $y=0$ in the equation and solve for $x$.

Example: Find the intercepts for the equation $4x - 5y = 20$.

  • Find y-intercept (set x = 0): $4(0) - 5y = 20$ $-5y = 20$ $y = -4$ The y-intercept is at the point $(0, -4)$.
  • Find x-intercept (set y = 0): $4x - 5(0) = 20$ $4x = 20$ $x = 5$ The x-intercept is at the point $(5, 0)$.
21

A line is described by the linear equation $7x - 4y = -56$. Determine the x-intercept and y-intercept of this line.

x-intercept: $-7$, y-intercept: $4$

x-intercept: $8$, y-intercept: $-14$

x-intercept: $-8$, y-intercept: $14$

x-intercept: $14$, y-intercept: $-8$
22

What is the slope of the line shown in the graph? You can use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

$1$

$\frac{1}{2}$

$2$

$-2$
23

Determine the slope of the line depicted in the graph. Remember that slope is 'rise over run'.

$-\frac{1}{2}$

$2$

$-2$

$3$
24

Find the slope of the line passing through the points shown on the graph.

$\frac{2}{3}$

$\frac{3}{2}$

$-\frac{2}{3}$

$2$
25

Calculate the slope of the line shown in the Cartesian plane.

$2$

$-\frac{1}{2}$

$-2$

$\frac{1}{2}$
26

What is the slope of the horizontal line presented in the graph?

Undefined

$0$

$2$

$1$
27

A straight line on a Cartesian plane passes through the points $(2, 3)$ and $(4, 7)$. What is the slope of the line? Remember that slope is calculated as the 'rise' (change in y) divided by the 'run' (change in x).

$5$

$2$

$\frac{1}{2}$

$-2$
28

Consider a line that passes through the points $(-1, 5)$ and $(2, -1)$. Using the formula for slope, $m = \frac{\text{rise}}{\text{run}}$, determine the slope of this line.

$2$

$\frac{1}{2}$

$-\frac{1}{2}$

$-2$
29

Find the slope of a line that goes through the points $(0, 1)$ and $(3, 3)$. Calculate the rise and the run to find your answer.

$\frac{3}{2}$

$2$

$3$

$\frac{2}{3}$
30

What is the slope of a horizontal line that passes through the points $(-4, 6)$ and $(5, 6)$? Think about what the 'rise' would be for a horizontal line.

$9$

Undefined

$0$

$1$
31

A vertical line passes through the points $(3, -2)$ and $(3, 4)$. What is the slope of this line? Consider what happens when you calculate the 'run'.

$1$

Undefined

$0$

$-1$
32

A straight line is drawn on a Cartesian plane. It passes through the points $(1, 2)$ and $(3, 6)$. What is the slope of this line?

$-\frac{1}{2}$

$\frac{1}{2}$

$-2$

$2$
33

Consider a line graphed on a coordinate plane that goes through the points $(-1, 5)$ and $(1, 1)$. Determine the slope of the line.

$\frac{1}{2}$

$2$

$-2$

$-\frac{1}{2}$
34

A line on a graph passes through the origin $(0, 0)$ and the point $(4, 3)$. What is the slope of the line?

$-\frac{3}{4}$

$1$

$\frac{4}{3}$

$\frac{3}{4}$
35

Find the slope of a line that is visualized on a Cartesian plane passing through the points $(-2, 4)$ and $(4, 1)$.

$2$

$-\frac{1}{2}$

$-2$

$\frac{1}{2}$
36

A horizontal line is shown on a graph. It passes through the points $(-3, 5)$ and $(2, 5)$. What is the slope of this line?

$0$

$5$

$1$

Undefined

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