Math / Algebra

QuestionTHIS IS A PRACTICE TEST $2 \square$ Mark for Review (45)
A line in the $x y$ -plane has a slope of $\frac{1}{9}$ and passes through the point $(0,14)$ . Which equation represents this line? (A) $y=-\frac{1}{9} x-14$ (B) $y=-\frac{1}{9} x+14$ (C) $y=\frac{1}{9} x-14$
D $y=\frac{1}{9} x+14$

Studdy Solution

STEP 1

1. The line has a slope of $\frac{1}{9}$ .
2. The line passes through the point $(0, 14)$ .
3. We are looking for the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Identify the slope and y-intercept.
2. Write the equation of the line using the slope-intercept form.
3. Match the equation to the given options.

STEP 3

Identify the slope and y-intercept.
The slope $m$ is given as $\frac{1}{9}$ .
The line passes through the point $(0, 14)$ , which means the y-intercept $b$ is $14$ .

STEP 4

Write the equation of the line using the slope-intercept form $y = mx + b$ .
Substitute the values of $m$ and $b$ into the equation:
$y = \frac{1}{9}x + 14$

STEP 5

Match the equation to the given options.
The equation $y = \frac{1}{9}x + 14$ matches option (D).
The correct equation representing the line is:
$\boxed{y = \frac{1}{9}x + 14}$

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QuestionTHIS IS A PRACTICE TEST $2 \square$ Mark for Review (45)
A line in the $x y$ -plane has a slope of $\frac{1}{9}$ and passes through the point $(0,14)$ . Which equation represents this line? (A) $y=-\frac{1}{9} x-14$ (B) $y=-\frac{1}{9} x+14$ (C) $y=\frac{1}{9} x-14$
D $y=\frac{1}{9} x+14$

Studdy Solution

STEP 1

1. The line has a slope of $\frac{1}{9}$ .
2. The line passes through the point $(0, 14)$ .
3. We are looking for the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Identify the slope and y-intercept.
2. Write the equation of the line using the slope-intercept form.
3. Match the equation to the given options.

STEP 3

Identify the slope and y-intercept.
The slope $m$ is given as $\frac{1}{9}$ .
The line passes through the point $(0, 14)$ , which means the y-intercept $b$ is $14$ .

STEP 4

Write the equation of the line using the slope-intercept form $y = mx + b$ .
Substitute the values of $m$ and $b$ into the equation:
$y = \frac{1}{9}x + 14$

STEP 5

Match the equation to the given options.
The equation $y = \frac{1}{9}x + 14$ matches option (D).
The correct equation representing the line is:
$\boxed{y = \frac{1}{9}x + 14}$

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Studdy Solution

STEP 1

1. The line has a slope of 19\frac{1}{9}91​.2. The line passes through the point (0,14)(0, 14)(0,14).3. We are looking for the equation of the line in the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

1. Identify the slope and y-intercept.2. Write the equation of the line using the slope-intercept form.3. Match the equation to the given options.

STEP 3

Identify the slope and y-intercept.The slope mmm is given as 19\frac{1}{9}91​.The line passes through the point (0,14)(0, 14)(0,14), which means the y-intercept bbb is 141414.

STEP 4

Write the equation of the line using the slope-intercept form y=mx+by = mx + by=mx+b.Substitute the values of mmm and bbb into the equation:y=19x+14 y = \frac{1}{9}x + 14 y=91​x+14

STEP 5

Match the equation to the given options.The equation y=19x+14y = \frac{1}{9}x + 14y=91​x+14 matches option (D). The correct equation representing the line is:y=19x+14 \boxed{y = \frac{1}{9}x + 14} y=91​x+14​

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1. The line has a slope of $\frac{1}{9}$ .
2. The line passes through the point $(0, 14)$ .
3. We are looking for the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

1. Identify the slope and y-intercept.
2. Write the equation of the line using the slope-intercept form.
3. Match the equation to the given options.

Identify the slope and y-intercept.
The slope $m$ is given as $\frac{1}{9}$ .
The line passes through the point $(0, 14)$ , which means the y-intercept $b$ is $14$ .

Write the equation of the line using the slope-intercept form $y = mx + b$ .
Substitute the values of $m$ and $b$ into the equation:
$y = \frac{1}{9}x + 14$

Match the equation to the given options.
The equation $y = \frac{1}{9}x + 14$ matches option (D).
The correct equation representing the line is:
$\boxed{y = \frac{1}{9}x + 14}$