Question

A line has slope 5/6 and y–intercept −3.
Which answer is the equation of the line?

A. y = −3x + 5/6

B. y = 3x + 5/6

C. y = 5/6x + 3

D. y = 5/6x − 3

Answer 1

A line passes through (−1, 7) and (2, 10).
Which answer is the equation of the line?

A. −3x + y = 4

B. −x + y = 12

C. −x + y = 8

D. −3x + y = 16

Answer 2

There are 3 in. of snow on the ground when it begins to snow 0.5 in/h.
Which linear equation represents the total depth of the snow, in inches, after x hours?

A. y = 0.5x + 3

B. y = 0.5x

C. 3 + y = 0.5x

D. x = 0.5y

Answer 3

To find the equation of the line given the slope and y-intercept, we can use the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

In this case, the slope \( m \) is \( \frac{5}{6} \) and the y-intercept \( b \) is \( -3 \).

Plugging in these values, we get:

\[ y = \frac{5}{6}x - 3 \]

Now, we can compare this with the options provided:

A. \( y = -3x + \frac{5}{6} \)

B. \( y = 3x + \frac{5}{6} \)

C. \( y = \frac{5}{6}x + 3 \)

D. \( y = \frac{5}{6}x - 3 \)

The correct answer is:

**D. \( y = \frac{5}{6}x - 3 \)**

Answer 4

To find the equation of the line passing through the points \((-1, 7)\) and \((2, 10)\), we first need to calculate the slope (\(m\)) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \((x_1, y_1) = (-1, 7)\) and \((x_2, y_2) = (2, 10)\).

Substituting the values:

\[
m = \frac{10 - 7}{2 - (-1)} = \frac{3}{3} = 1
\]

Now we have the slope \(m = 1\).

Next, we can use the point-slope form of the line equation, which is:

\[
y - y_1 = m(x - x_1)
\]

Using point \((-1, 7)\):

\[
y - 7 = 1(x - (-1))
\]
\[
y - 7 = 1(x + 1)
\]
\[
y - 7 = x + 1
\]
\[
y = x + 8
\]

Now, we can convert this equation into standard form \(Ax + By = C\):

\[
-x + y = 8
\]

Now let's compare with the given options:

A. \( -3x + y = 4 \)

B. \( -x + y = 12 \)

C. \( -x + y = 8 \)

D. \( -3x + y = 16 \)

The correct answer is:

**C. \( -x + y = 8 \)**

Answer 5

To represent the total depth of the snow (in inches) after \( x \) hours, we need to take into account both the initial depth of the snow and the rate at which it is snowing.

1. **Initial depth of snow**: 3 inches
2. **Rate of snowfall**: 0.5 inches per hour

The total depth of snow \( y \) after \( x \) hours can be expressed as:

\[
y = \text{initial depth} + (\text{rate of snowfall} \times \text{time})
\]

So, the equation becomes:

\[
y = 3 + 0.5x
\]

or equivalently:

\[
y = 0.5x + 3
\]

Now we can compare this equation to the given options:

A. \( y = 0.5x + 3 \)

B. \( y = 0.5x \)

C. \( 3 + y = 0.5x \)

D. \( x = 0.5y \)

The correct answer is:

**A. \( y = 0.5x + 3 \)**