Question

Use algebra to find the point at which the line f ( x ) = (9)/(2) x + (191)/(8) intersects the line h ( x ) = (9)/(5) x + (221)/(20) . Write the values of x and y as reduced fractions or integers.

Answer 1

To find the point of intersection between the lines f(x) = (9/2)x + (191/8) and h(x) = (9/5)x + (221/20), we set the equations equal to each other and solve for x and y. The point of intersection is (-57/2, 41/4).

Step-by-step explanation:

To find the point of intersection between two lines, we need to set the equations equal to each other and solve for the values of x and y. So, we set the equations f(x) = (9/2)x + (191/8) and h(x) = (9/5)x + (221/20) equal to each other:

(9/2)x + (191/8) = (9/5)x + (221/20)

To solve for x, we first eliminate the fractions by multiplying both sides of the equation by 40:

20(9/2)x + 20(191/8) = 40(9/5)x + 40(221/20)

After simplifying, we get:

90x + 955 = 72x + 442

Subtracting 72x from both sides, we have:

18x + 955 = 442

Subtracting 955 from both sides, we get:

18x = -513

Dividing both sides by 18, we find that x = -513/18, which simplifies to x = -57/2.

To find the value of y, we substitute the value of x back into either of the original equations. Let's use the equation for f(x):

f(x) = (9/2)x + (191/8)

Substituting x = -57/2, we have:

f(-57/2) = (9/2)(-57/2) + (191/8)

After simplifying, we find that y = 82/8, which reduces to y = 41/4.

Therefore, the point of intersection is (x, y) = (-57/2, 41/4).