Pls help. The question is :
Blake the rabbit has a ramp with equation 2y + x = 7.
His friend at the pet shop has a ramp with equation y = 12 – 0.5x.
Will the rabbits ever meet?
2y+x=7
y+.5x=12
change second equation to
2y+x=24
now the ramps are same slope, of course there is not an intersection.
Can you explain this further please, I don't understand
To determine if the rabbits will ever meet, we need to find the point where the two ramp equations intersect.
First, let's set up a system of equations using the given ramp equations:
1) 2y + x = 7
2) y = 12 - 0.5x
To solve this system, we can use the substitution method.
Step 1: Solve equation 2 for y:
y = 12 - 0.5x
Step 2: Substitute the value of y from equation 2 into equation 1:
2(12 - 0.5x) + x = 7
Step 3: Simplify:
24 - x + x = 7
24 = 7
Step 4: Since 24 does not equal 7, the two ramp equations do not intersect at any point.
Therefore, Blake and his friend's rabbits will never meet on their ramps.
To find out if the rabbits will meet, we need to determine if the two ramp equations intersect.
First, let's rewrite the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
For Blake's ramp:
2y + x = 7
2y = -x + 7
y = -0.5x + 3.5
For the pet shop's ramp:
y = 12 - 0.5x
Now that we have the equations in slope-intercept form, we can compare the slopes. The slopes represent the rate at which y changes with respect to x.
The slope of Blake's ramp equation (-0.5) and the slope of the pet shop's ramp equation (-0.5) are the same. Since their slopes are equal, the ramps are parallel lines and will never intersect.
Therefore, Blake and his friend's rabbits will not meet.