Math / Geometry

Question15) Find the slope and $y$ -intercept from the following graph of a linear equation. (A) slope $=4$ and $y$ -intercept $=3$ (B) slope $=3$ and $y$ -intercept $=4$ (C) slope $=4$ and $y$ -intercept $=5$ (D) slope $=5$ and $y$ -intercept $=4$

Studdy Solution

STEP 1

1. The line is linear and can be represented by the equation $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.
2. The points given are $(0, -1)$ and $(1, 4)$ .

STEP 2

1. Calculate the slope of the line.
2. Determine the $y$ -intercept from the graph.
3. Match the calculated values to the given options.

STEP 3

Calculate the slope of the line using the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(0, -1)$ and $(1, 4)$ :
$m = \frac{4 - (-1)}{1 - 0}$ $= \frac{4 + 1}{1}$ $= \frac{5}{1}$ $= 5$

STEP 4

Determine the $y$ -intercept from the graph. The $y$ -intercept is the point where the line crosses the $y$ -axis. From the given point $(0, -1)$ , the $y$ -intercept is:
$b = -1$

STEP 5

Match the calculated slope and $y$ -intercept to the given options. The calculated slope is $5$ and the $y$ -intercept is $-1$ . None of the provided options match these values exactly. Therefore, none of the options (A), (B), (C), or (D) are correct based on the given graph.

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Question15) Find the slope and $y$ -intercept from the following graph of a linear equation. (A) slope $=4$ and $y$ -intercept $=3$ (B) slope $=3$ and $y$ -intercept $=4$ (C) slope $=4$ and $y$ -intercept $=5$ (D) slope $=5$ and $y$ -intercept $=4$

Studdy Solution

STEP 1

1. The line is linear and can be represented by the equation $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.
2. The points given are $(0, -1)$ and $(1, 4)$ .

STEP 2

1. Calculate the slope of the line.
2. Determine the $y$ -intercept from the graph.
3. Match the calculated values to the given options.

STEP 3

Calculate the slope of the line using the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(0, -1)$ and $(1, 4)$ :
$m = \frac{4 - (-1)}{1 - 0}$ $= \frac{4 + 1}{1}$ $= \frac{5}{1}$ $= 5$

STEP 4

Determine the $y$ -intercept from the graph. The $y$ -intercept is the point where the line crosses the $y$ -axis. From the given point $(0, -1)$ , the $y$ -intercept is:
$b = -1$

STEP 5

Match the calculated slope and $y$ -intercept to the given options. The calculated slope is $5$ and the $y$ -intercept is $-1$ . None of the provided options match these values exactly. Therefore, none of the options (A), (B), (C), or (D) are correct based on the given graph.

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Question15) Find the slope and yyy-intercept from the following graph of a linear equation. (A) slope =4=4=4 and yyy-intercept =3=3=3 (B) slope =3=3=3 and yyy-intercept =4=4=4 (C) slope =4=4=4 and yyy-intercept =5=5=5 (D) slope =5=5=5 and yyy-intercept =4=4=4

Studdy Solution

STEP 1

1. The line is linear and can be represented by the equation y=mx+b y = mx + b y=mx+b, where m m m is the slope and b b b is the y y y-intercept.2. The points given are (0,−1)(0, -1)(0,−1) and (1,4)(1, 4)(1,4).

STEP 2

1. Calculate the slope of the line.2. Determine the y y y-intercept from the graph.3. Match the calculated values to the given options.

STEP 3

STEP 4

Determine the y y y-intercept from the graph. The y y y-intercept is the point where the line crosses the y y y-axis. From the given point (0,−1)(0, -1)(0,−1), the y y y-intercept is:b=−1 b = -1 b=−1

STEP 5

Match the calculated slope and y y y-intercept to the given options. The calculated slope is 5 5 5 and the y y y-intercept is −1-1−1. None of the provided options match these values exactly. Therefore, none of the options (A), (B), (C), or (D) are correct based on the given graph.

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Question15) Find the slope and $y$ -intercept from the following graph of a linear equation. (A) slope $=4$ and $y$ -intercept $=3$ (B) slope $=3$ and $y$ -intercept $=4$ (C) slope $=4$ and $y$ -intercept $=5$ (D) slope $=5$ and $y$ -intercept $=4$

1. The line is linear and can be represented by the equation $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.
2. The points given are $(0, -1)$ and $(1, 4)$ .

1. Calculate the slope of the line.
2. Determine the $y$ -intercept from the graph.
3. Match the calculated values to the given options.

Determine the $y$ -intercept from the graph. The $y$ -intercept is the point where the line crosses the $y$ -axis. From the given point $(0, -1)$ , the $y$ -intercept is:
$b = -1$

Match the calculated slope and $y$ -intercept to the given options. The calculated slope is $5$ and the $y$ -intercept is $-1$ . None of the provided options match these values exactly. Therefore, none of the options (A), (B), (C), or (D) are correct based on the given graph.