Luis and Raul are riding their bicycles to the beach from their respective homes. Luis proposes that they leave their respective homes at the same time and plan to arrive at the beach at the same time. The diagram shows​ Luis's position at two points during his ride to the beach. Write an equation in​ slope-intercept form to represent​ Luis's ride from his house to the beach. If Raul lives 5 miles closer to the beach than​ Luis, at what speed must Raul ride for the plan to​ work?


If x represents the time in hours since the ride began and y represents the remaining distance from the​ beach, then the equation

_____



represents​ Luis's ride from his house to the beach.

Answer:

equation: y=-7.5x+15 and Raul must ride at a speed of 5 mi/hr

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex] to find out the slope. [tex]\frac{6-11.25}{1.2-0.5}[/tex]=[tex]\frac{-5.25}{0.7} = -7.5[/tex]

Then you fill x and y to find out the y intercept

[tex]11.25=-7.5*0.5+b[/tex]

[tex]11.25=-3.75+b\\11.25+3.75=15\\[/tex]

Y intercept= 15

then you put it in the equation:

y=-7.5x+15

Since Raul lives 5 miles closer and Luis is 5 miles away, he needs to go at 5 miles an hour to get to the spot.

That is 5 miles/hour

The distance and time, as presented in this question are illustrations of linear equations.

From the diagram, we have:

[tex](x_1,y_1) = (0.5,11.25)[/tex]

[tex](x_2,y_2) = (1.2,6)[/tex]

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{6 - 11.25}{1.2 - 0.5}[/tex]

[tex]m = \frac{-5.25}{0.7}[/tex]

[tex]m = -7.5[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives

[tex]y = -7.5(x - 0.5) + 11.25[/tex]

[tex]y = -7.5x + 3.75 + 11.25[/tex]

[tex]y = -7.5x + 15[/tex]

Calculate distance, when [tex]x = 5[/tex]

We have:

[tex]y = -7.5 \times 5 + 15[/tex]

[tex]y = -22.5[/tex]

The speed (s) is then calculated as:

[tex]s = \frac{22.5}{5}[/tex]

[tex]s = 4.5[/tex]

Hence, he must plan to ride at 4.5 miles per hour

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