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Exercises Graphs and straight lines

Example 11.15 from Prealgebra, 11.2 Graphing Linear Equations

Graphing Linear Equations: example 11.15

The graph of $y = 2 x - 3$ is shown below.

For each ordered pair decide

ⓐ Is the ordered pair a solution to the equation?
ⓑ Is the point on the line?

(a) $(0, 3)$
(b) $(3, - 3)$
(c) $(2, - 3)$
(d) $(- 1, - 5)$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Substitute the $x$ - and $y$ -values into the equation to check if the ordered pair is a solution to the equation.
ⓐ

ⓑ Plot the points A: $y = 2 x - 3$ B: $(2, - 3)$ C: $(2, - 3)$ and D: $(- 1, - 5)$ .
The points $(0, - 3)$ , $(3, 3)$ , and $(- 1, - 5)$ are on the line $y = 2 x - 3$ , and the point $(2, - 3)$ is not on the line.

The points which are solutions to $y = 2 x - 3$ are on the line, but the point which is not a solution is not on the line.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The graph of $y = 3 x - 1$ is shown.

For each ordered pair, decide

ⓐ is the ordered pair a solution to the equation?
ⓑ is the point on the line?

$(0, - 1)$
$(2, 2)$
$(3, - 1)$
$(- 1, - 4)$

How did it go?

PreviousUse the Rectangular Coordinate System: example 11.14 Next Graphing Linear Equations: example 11.16

From Prealgebra (1st edition) by OpenStax (Rice University), section 11.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.