Question

Y = four-thirds x minus 10.7

a. slope =four-thirds x y-intercept is (0, 10.7)
b. slope =four-thirds y-intercept is (0, -10.7)
c. slope =four-thirds y-intercept is (0, 10.7)
d. slope = -10.7 y-intercept is four-thirds

Answer 1

The equation
`\(y = (4)/(3)x - 10.7\)` has a slope of
`\((4)/(3)\)`, signifying a change of
`((4)/(3)\))` in y per unit change in x with a y-intercept of (0, -10.7).

Certainly! Let's break down the given equation
`\(y = (4)/(3)x - 10.7\)` to identify the slope and y-intercept.

1. **Identify the Slope m:**

- The coefficient of x in the equation represents the slope (\(m\)).

- In this case,
`\(m = (4)/(3)\).`

2. **Identify the Y-intercept b:**

- The constant term in the equation is the y-intercept (\(b\)).

- In this case, b = -10.7.

3. **Form the Slope-Intercept Form:**

- Write the equation in the form y = mx + b using the identified values.

- The equation is now
`\(y = (4)/(3)x - 10.7\).`

4. **Interpretation:**

- The slope m is the ratio of the change in \(y\) to the change in \(x\). Here, for every one-unit increase in x, y increases by
`\((4)/(3).`

- The y-intercept b is the point where the graph intersects the y-axis, and in this case, it is (0, -10.7).

Therefore, the correct interpretation is that the slope is \(\frac{4}{3}\), and the y-intercept is (0, -10.7).