- A store buys a jacket for $20.00 and then sells it to customers for 80% more than that. What is the selling price of the jacket?
a. $16.00
b. $24.00
c. $28.00
d. $36.00
- Eva draws a line that includes the points (2,0) and (-2,2). Which function gives all the points (x,y) on this line? y=-(1)/(2)x+1 y=-2x+1,y=2x-1
The correct answer and explanation is:
Question 1:
The store buys the jacket for $20.00 and sells it for 80% more than the cost price.
To calculate the selling price:
- Find 80% of $20.00:
20.00×0.80=16.0020.00 \times 0.80 = 16.00 - Add this to the cost price:
20.00+16.00=36.0020.00 + 16.00 = 36.00
Answer: d. $36.00
Question 2:
Eva draws a line that passes through the points (2, 0) and (-2, 2). To find the equation of this line:
- Calculate the slope (m): The formula for slope is: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1} Using the points (−2,2)(-2, 2) and (2,0)(2, 0): m=2−0−2−2=2−4=−12m = \frac{2 – 0}{-2 – 2} = \frac{2}{-4} = -\frac{1}{2}
- Find the y-intercept (b): Use the slope-intercept form of a line: y=mx+by = mx + b Substitute one point, say (2,0)(2, 0), and m=−12m = -\frac{1}{2}: 0=−12(2)+b ⟹ 0=−1+b ⟹ b=10 = -\frac{1}{2}(2) + b \implies 0 = -1 + b \implies b = 1
- Write the equation: Substituting m=−12m = -\frac{1}{2} and b=1b = 1, the equation of the line is: y=−12x+1y = -\frac{1}{2}x + 1
Answer: y=−12x+1y = -\frac{1}{2}x + 1
Explanation :
The function y=−12x+1y = -\frac{1}{2}x + 1 represents the line passing through the points (2, 0) and (-2, 2). To derive this, we first calculate the slope mm, which measures the steepness of the line and is found by dividing the change in yy-values by the change in xx-values. For the given points, the slope is −12-\frac{1}{2}, indicating the line decreases as xx increases.
Next, the y-intercept bb is determined. It is the value of yy when x=0x = 0. Using one of the given points and solving for bb, we find it equals 1. The slope-intercept form y=mx+by = mx + b allows us to represent the relationship between xx and yy on the line.
Finally, the function y=−12x+1y = -\frac{1}{2}x + 1 gives all the points on the line because any xx-coordinate substituted into this equation will yield the corresponding yy-coordinate. Verifying with the given points confirms the accuracy of this equation, as both (2,0)(2, 0) and (−2,2)(-2, 2) satisfy it.