Question

Creat a word problem for 6x + 8y = 24 and then determine the slope, x, and y-intercept.

Answer 1

Step 1:

The equation is .

Create a word problem.

Sammi purchased  pens and  chocolates and the total amount spent for purchasing both items is $24.

1) Write an equation to represent the situation.

2) Find the slope of the equation.

3) Find the -intercept and -intercept of the equation.

Step 2:

Let  be the cost of each pen.

Let  be the cost of each chocolate.

Amount spent by Sammi for pens is .

Amount spent by Sammi for Chocolates is .

Total amount spent by Sammi is .

Therefore the equation is .

The slope intercept form is , where  is slope and  is the -intercept.

Convert the equation into slope-intercept form of line equation.

Subtract  from each side.

Apply additive inverse property .

Divide each side by 8.

.

Compare the equation with slope intercept form of line equation.

Here  and .

Therefore, the slope of the line equation is .

The -intercept is .

Step 3:

Find the -intercept by substituting  in .

.

The -intercept is .

Solution:

The slope of the equation is .

-intercept is  and -intercept is .