What is an equation for the line with slope 2/3 and y-intercept 9?

A. Y=2/3x B. y=9x C. Y=2/3x+9
D. y= 9x+2/3

Q2. Suppose Y varies directly with X, and Y=24 when x=8. what is the value of Y when x =10.
A. 10 B. 30 C. 80 D. 240
.

the slope-intercept rule is called that for a reason...

Q2. y=kx, so y/x=k, a constant. You want y such that

y/10 = 24/8

A1. The equation for the line with slope 2/3 and y-intercept 9 is option C. Y = 2/3x + 9.

A2. If Y varies directly with X, we can set up the equation Y = kX, where k is the constant of variation. Given that Y = 24 when X = 8, we can substitute these values into the equation to solve for k: 24 = k * 8. Dividing both sides by 8, we get k = 3. So the equation is Y = 3X.

To find the value of Y when X = 10, we can substitute this value into the equation: Y = 3 * 10 = 30. Therefore, the value of Y when X = 10 is option B. 30.

To find the equation for a line with slope and y-intercept, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.

For the first question, the slope is given as 2/3 and the y-intercept is given as 9. So the equation for the line can be written as y = (2/3)x + 9. Therefore, the correct answer is C. Y = (2/3)x + 9.

For the second question, if Y varies directly with X, it means that the ratio of Y to X remains constant. This can be written in the form of an equation Y = kX, where k is the constant of variation.

Given that Y = 24 when X = 8, we can substitute these values into the equation Y = kX to find the value of k. Thus, 24 = k * 8. Solving for k, we get k = 3.

Now that we know the constant of variation, we can use the equation Y = kX to find the value of Y when X = 10: Y = 3 * 10 = 30. Therefore, the correct answer is B. 30.