You're given the slope of the line and a point thru which the line passes. So it makes sense to use the point-slope form of the equation of a straight line: if the point is (a,b) and the slope is m, then
y-b=m(x-a). You'd then solve this for y to obtain the equation in slope-intercept form.
On the other hand, if you're asked to write the equation in slope-intercept form, starting with the general form of this equation may be faster: y=mx+b.
Substitute the given values for x and y (which are 25 and -9) and m (which is (2/5). Solve the resulting equation for b (the y-intercept).
Then write the finished equation: y=( ? )x + b, where b is the y-intercept you've just found.
Answer:
19 red beads
Step-by-step explanation:
We first need to find a common denominator of 4/9, 1/5 and 1/4.
The common denominator is 180. Like in an expression, what we do to one side we have to do to the other.
Silver - 180/9 = 20 ; 20*4 = 80 so there are roughly 80 sliver beads.
Gold - 180/5 = 36 ; 36*1 = 36 so there are roughly 36 gold beads.
Blue - 180/4 = 45 ; 45*1 = 45 so there are roughly 56 blue beads.
180 - (silver+gold+blue) = red beads
180-161 = 19 red beads b/c ----->
80+36+45+19 = 180
when two numbers have the same variable, we can add and subtract just like normal numbers.
12x + 8x = 20x - 3x = 17x
Using the slope - intercept relation, the required equation which models the scenario and Raul's speed are ;
- <em>y</em><em> </em><em>=</em><em> </em><em>-</em><em> </em><em>7.5x</em><em> </em><em>+</em><em> </em><em>15</em><em> </em>
- <em>4</em><em> </em><em>miles</em><em> </em><em>per</em><em> </em><em>hour</em><em> </em>
Time difference, Δt = 1.2 hours - 0.5 hours = 0.7 hours
Change in distance, Δd = 11.25 - 6 = 5.25 miles
Assuming a constant speed :
- Speed = (Δd ÷ Δt) = (5.25 ÷ 0.7) = 7.5 mi/hr
<u>Using the general form</u> :
At, x = 1.2 hours ;
Miles left, y = 6 miles
End point decreases by 7.5 mi/hr (-7.5 mi/hr)
Inputting the data into the equation :
6 = - 7.5(1.2) + c
6 = - 9 + c
c = 6 + 9 = 15 miles
<u>The expression in slope intercept form becomes</u> ;
<u>If Raul lives 5 miles closer to the beach</u> ;
<u>Time it will take Luis to get to the beach</u> :
- Time taken = (15 ÷ 7.5) = 2.5 hours
Distance Raul has to cover = 15 - 5 = 10 miles
To reach the beach after 2.5 hours ;
- Speed required = (10 ÷ 2.5) = 4 mi/hr
Therefore, Raul has to ride at 4 miles per hour for the plan to work.
Learn more :brainly.com/question/18405415
