• Find the value of a variable that satisfies an equation
• Write equations for lines using different forms: slope-intercept, point-slope, and standard form
• Recognize and write equations for horizontal and vertical lines
• Determine if lines are parallel or perpendicular, and write equations for lines parallel or perpendicular to a given line

The chief financial officer, or CFO, of a company is in charge of financial planning, risk management, budgeting, record keeping, and reporting. Dhakiya is the CFO of a non-profit community arts center.

One of Dhakiya’s responsibilities is to track the sales of fundraising merchandise. She is hoping to raise [latex]$2000[/latex] in the month of February with sales of merchandise averaging [latex]$75[/latex] a day. If [latex]y[/latex] represents the total money raised in [latex]x[/latex] days of sales, Dhakiya can use a linear equation to model the fundraiser.

The fundraising merchandise was created by volunteers using mostly repurposed or donated materials. This way, Dhakiya was able to keep the overhead costs for this fundraiser fairly low. The [latex]y[/latex]-intercept indicates the overhead cost of materials for the merchandise that will be deducted from the total sales.

Another one of Dhakiya’s responsibilities is applying for grants to fund activities for the youth programs at the community arts center. Dhakiya is applying to two grants that each offer a starting amount and additional funds based on the number of participants in the youth programs. The following equations represent the total funding provided, [latex]y[/latex], given [latex]x[/latex] participants in the youth programs.

• Grant 1: [latex]y=40(x+25)[/latex]
• Grant 2: [latex]-80x+2y=1600[/latex]

After analyzing the community art center’s energy bills, Dhakiya determined the best plan for the polymer clay workshops that conserves energy. Ovens are used to bake the sculptures created in the workshops, and if all of the baking is done consecutively, the ovens only have to preheat once. Also, if the workshops are held in months with cooler temperatures, the ovens will contribute to heating the sculpture studio to a comfortable temperature, reducing the energy that the studio’s heaters will need to use. She found that the total kilowatt-hours of energy, [latex]y[/latex], used by the ovens for [latex]x[/latex] hours of baking time is given by

[latex]y=2x+0.5[/latex]

The equation for the kilowatt-hours of energy, [latex]y[/latex], that the heaters would use to maintain a comfortable ambient temperature in the studio after [latex]x[/latex] hours of baking time is perpendicular to the equation above.