Question

1. a line passes through the point (- 2, 5) and has a slope of \\(\frac{-1}{2}\\). write the equation using the point slope form of this line. (2 pts)

1. sara took a taxi cab from the airport to her convention center for her job. she is presenting on ai usage in schools and paid $11.50. the equation for the taxi cab fare can be modeled by a linear relationship. the equation \\(y = 0.50x + 5\\) models the total fare, \\(y\\), of her trip for \\(x\\) miles.

a. how much did it cost sara to get into the cab? explain. (2 pts)

b. according to the model, how much does it cost per mile? explain (2 pts)

1. write an equation in slope intercept form for the linear relationship shown on the graph. (2 pts)

(graph with points (-1, 10) and (3, 2))

Explanation:

Question 4

Step1: Recall point - slope form

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.
We are given that the line passes through the point \((- 2,5)\) (so \(x_1=-2\) and \(y_1 = 5\)) and has a slope \(m=-\frac{1}{2}\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-2\), \(y_1 = 5\) and \(m =-\frac{1}{2}\) into the point - slope formula:
\(y-5=-\frac{1}{2}(x - (-2))\)
Simplify the right - hand side: \(y - 5=-\frac{1}{2}(x + 2)\)

The cost to get into the cab is the fixed cost, which occurs when the number of miles \(x = 0\) (since no miles have been traveled yet). In the linear equation \(y=mx + b\) (where \(y\) is the total cost, \(m\) is the cost per mile, \(x\) is the number of miles, and \(b\) is the fixed cost), when \(x = 0\), \(y=b\). For the equation \(y = 0.50x+5\), when \(x = 0\), \(y=5\). So the cost to get into the cab is the value of \(y\) when \(x = 0\), which is \(\$5\).

In the linear equation \(y=mx + b\) (where \(y\) is the total cost, \(m\) is the cost per mile, \(x\) is the number of miles, and \(b\) is the fixed cost), the coefficient of \(x\) is the cost per mile. For the equation \(y = 0.50x+5\), the coefficient of \(x\) is \(0.50\). So the cost per mile is \(\$0.50\).

Answer:

\(y - 5=-\frac{1}{2}(x + 2)\)

Question 5a