Question

The linear function f(x) passes through the points (0, 5) and (2, 7) . A few values from the exponential function g(x) are shown in the table.

x g(x)
−1 25
2 50
3 250

What is the positive difference in the y-intercept value of f(x) ​and g(x) ? Enter your answer in the box.

Answer 1

the correct answer is 3

Explanation:

Answer 2

Answer: 3

Explanation:

The linear function f(x) passes through (0, 5) and (2, 7). Choose a point and find the slope. Then input the point and slope into the Point-Slope formula. Then solve for "y", which puts it in the slope-intercept form (y = mx + b)

slope (m) =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

=
`(7-5)/(2-0)`

=
`(2)/(2)`

= 1

Point-Slope:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

↓

y-intercept = 5

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x | g(x)

-1 | 2/5

2 | 50

3 | 250

y = 2(5)ˣ

y = 2(5)⁰

= 2(1)

= 2

y-intercept = 2

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The difference between the y-intercepts of f(x) and g(x) is 5 - 2 = 3