Mathematics > EXAM > Sophia Learning, College Algebra, Milestone 3, WITH ANSWERS (All)

Sophia Learning, College Algebra, Milestone 3, WITH ANSWERS 1 The graph of a linear function passes through the points and . Find the slope of this function. • • • �... �� CORRECT RATIONALE Since we have two points from a linear function, we can use the slope formula to find the slope of the line. The slope is the difference in coordinates from the two points divided by the difference in coordinates from the same two points. When plugging in the values it is important to be consistent with which coordinates are subtracted in the calculations. Now that the numbers are plugged in, evaluate the subtraction in both the numerator and the denominator. In the numerator, the difference in coordinates is minus , or . In the denominator, the difference in coordinates is minus , which is the same as plus , or . The slope of the line is . CONCEPT Determining Slope 2 The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below. A B Bread $2.20 $2.50 Milk $3.60 $3.40 Mary needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $44.20. At Supermarket B, she would pay $44.70. Which of the following system of equations represents this situation? • • CORRECT • • RATIONALE In general, the equation to represent the total cost of buying bread and milk would be the sum of the cost for bread and cost for milk. To find the cost of bread and milk, first define variables to represent the amount of bread and milk. Here, will represent bread, and will represent milk. Both and will be multiplied by their respective prices. At Store A, a loaf of bread costs $2.20, and a gallon of milk costs $3.60. We also know that the total cost at Store A is $44.20. So the total cost at Store A would be expressed with this equation. We can construct a similar equation for Store B. At Store B, bread cost $2.50 per loaf, and milk costs $3.40 per gallon. We also know that the total cost at Store B is $44.70. The total cost at Store B would be expressed with this equation. This is the system of equations to represent the costs of bread and milk at Store A and B. CONCEPT Writing a System of Linear Equations 3 Select the correct slope and y-intercept for the following linear equation: • CORRECT • • • • • RATIONALE Equations in the form allow us to easily identify the slope and y-intercept. The slope is given by the variable , and the y-intercept is given by the variable . The variable is the coefficient in front of x that represents the slope. In the equation , the coefficient in front of is , so is the slope. The variable represents the y-coordinate of the y- intercept. In the equation , 8 will be the y- coordinate of the y-intercept. Remember that the x- coordinate of the y-intercept is always 0, so the y- intercept is . CONCEPT Forms of Linear Equations 4 Consider the region shaded in yellow. Which inequality does the shaded region represent? • • • • CORRECT RATIONALE Writing a linear inequality from a graph is similar to writing a linear equation from a graph. The biggest difference is that with inequalities, a portion of the coordinate plane is highlighted to represent the solution region. Start by focusing on the line that we see. Determine the y- intercept and slope so that we can write an equation in slope-intercept form. The graph intercepts the y-axis at (0,3) so this is our intercept. To find the slope, we can use this point and another point on the line, for example, (-2,-1). Plugging these two points into the slope formula, we get a slope of 2. We can write an equation in the form y = mx + b, where m is the slope and b is the y-coordinate of the y-intercept. [Show More]

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