Question

Ace and Annie graphed linear equations on the same grid as shown below. Use their graphs to
answer a-d.
ACE
a. Write an equation to represent each person's line.
ACE:
ANNIE:
b. List the ordered pair where the lines intersect. S,3
c. Is the point above a solution to Ace's equation? Give two
ways you can tell.
'ANNIE
d. Is the point from part b also a solution to Annie's equation?
Give two ways you can tell.

Answer 1

Ace and Annies' graphs are illustrations of linear functions.

(a) Equation of each line

The points on Ace's line are: (0,2) and (7,9)

The slope (m) is calculated as:

$\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}$

So, we have:

$\mathbf{m = \frac{9 - 2}{7- 0} = 1}$

The equation is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

This gives

$\mathbf{y = 1(x - 0) + 2}$

$\mathbf{y = x + 2}$

The points on Annie's line are: (0,8) and (6,2)

The slope (m) is calculated as:

$\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}$

So, we have:

$\mathbf{m = \frac{2 - 8}{6- 0} = -1}$

The equation is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

This gives

$\mathbf{y = -1(x - 0) + 8}$

$\mathbf{y = -x + 8}$

So, we have:

• The equation of Ace's line is: $\mathbf{y = x + 2}$
• The equation of Annie's line is: $\mathbf{y = -x + 8}$

(b) The ordered pair where the lines intersect

The lines intersect at x = 3 and y = 5.

So, the ordered pair where the lines intersect is (3,5)

(c) Is the ordered pair a solution to Ace's equation

Yes, the ordered pair is a solution to Ace's equation

This is so because:

• The ordered pair satisfies the equation $\mathbf{y = x + 2}$
• The line of $\mathbf{y = x + 2}$ passes through the point

(d) Is the ordered pair a solution to Annie's equation

Yes, the ordered pair is a solution to Annie's equation

This is so because:

• The ordered pair satisfies the equation $\mathbf{y = -x + 8}$
• The line of $\mathbf{y =- x + 8}$ passes through the point

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