Question

James is participating in a 5-mile walk to raise money for a charity. he has received $200 in fixed pledges and raises $20 extra for every mile he walks. use a point-slope equation to find the amount he will raise ifhe completes the walk.

Answer 1

The standard formula of a point-slope equation is (y-y1) = m(x-x1). So, we would arrange the final equation in this way as much as possible. Let y be the total amount her receives and x be the number of miles. That would be

y = 200 + 20x
y = 20 (10 + x)

That would be the equation. If he finishes the walk,

y = 20 (10+5)
y = $300

he would receive a total of $300.

Answer 2

Answer:

The amount James will collect if he completes the walk is $ 300

Step-by-step explanation:

The line can be understood as an infinite set of points aligned in a single direction. A line can be expressed by an equation that follows the model y = m * x + b, where "x" e "y" are the variables in a plane. In this expression m is called the slope of the line and is related to the inclination of the line, and b is the independent term and is the value of the point at which the line cuts to the vertical axis (y axis) in the plane.

In general, the slope represents the variation of y with respect to the variation of x.  That is, if the value of "x" varies, the value of "y" will also vary. On the other hand, the value of "b", being the interserction with the y-axis, means that the value of "x" must be zero. Then it represents the initial condition of the problem. Then, in this case, James has initially received $ 200 in fixed commitments, 200 being the value of "b". James raises an additional $ 20 for every mile he walks, so the value of the "m" slope is 20 and "x" represents every mile James walks.

Finally, the equation of the line represented is:

y=20*x+200

One type of linear equation is the point-slope form, which provides the slope of a line and the coordinates of a point on it. The point-slope form of a linear equation is written as  

y-y1 = m (x-x1)  

where m is the slope and (x1, y1) are the coordinates of the point.

In this particular case, it was mentioned that the value of the slope is 20. The values of (x1, y1) must be known. In this case, James initially received $ 200 in fixed commitments, meaning that the value of x1 = 0 and the value of y1 = 200. Replacing these values in the desired equation you get:

y-200=20*(x-0)

y-200=20*x

To find the amount that will be collected if you complete the walk, you must replace the value of x (which represents each mile walked) by 5, the distance to travel on the walk:

y-200=20*5

y-200=100

y=100+200

y=300

The amount James will collect if he completes the walk is $ 300