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galben [10]
3 years ago
12

Miguel bikes 23 km per hour and starts at mile 10. Gabby bies 28 km per hour and starts at mile 0. Which system of linear equati

ons represents this situation?
Mathematics
1 answer:
pashok25 [27]3 years ago
5 0

Answer:

y = 23x + 10

y = 28x + 0

Step-by-step explanation:

Given that:

Miguel :

Velocity = 23 km/hr

Starting position = 10 miles

Gabby:

Velocity = 28 km/hr

Starting position = 0 miles

The general form of a linear equation :

y = mx + c

In the scenario above ; the starting points corresponds to the intercept, c

The distance moved per hour (velocity) is the slope (m), which is the change in y per unit change in x

Hence ;

Miguel:

y = 23x + 10

Gabby:

y = 28x + 0

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Any line can be expressed in the form y=mx+b where m is the slope and b is y intercept.

Two lines can either be parallel ,overlap or meet at one point .Let us look at different cases :

1)When two lines are parallel they do not intersect at any point and hence the system of equations have no solution.

2) When two lines overlap each other then the two lines touch each other at infinite number of points and we say the system of equations have infinite solutions.

3) When two lines intersect each other at one point we say the system of equation has one solution.

Part A:

The given lines are intersecting at one point so we have one solution.

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To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope (m):

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It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair x_{2} and the \frac{-1}{2} in the first ordered pair x_{1}.
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.

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Finally, to get the slope we can complete the fraction by dividing.

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The slope of this equation, m, is 7, and so far, our equation looks like this:

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The y-intercept of this line is 0.

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y=7x+0

Or, for neatness' sake, we can just say

y=7x

which is your final equation.

The line through (\frac{-1}{2},  \frac{-7}{2}) and (2, 14) in slope-intercept form is <span>y=7x.
Hope that helped! =) </span>


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