Math / Algebra

QuestionFind the slope and the $y$ -intercept of the graph of the linear equation.
1. $y=3 x+4$
2. $y=-5 x-1$
3. $y=\frac{2}{3} x-2$
4. $y+7=4 x$
5. $y-3=-6 x$
6. $y+9=\frac{3}{4} x$

Studdy Solution

STEP 1

1. Each equation is in or can be converted to the slope-intercept form of a linear equation, which is $y = mx + b$ .
2. In the slope-intercept form, $m$ represents the slope and $b$ represents the y-intercept.

STEP 2

1. Identify the slope and y-intercept for each equation already in slope-intercept form.
2. Rearrange equations that are not in slope-intercept form to identify the slope and y-intercept.

STEP 3

For the equation $y = 3x + 4$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $3$ . - The y-intercept $b$ is $4$ .

STEP 4

For the equation $y = -5x - 1$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $-5$ . - The y-intercept $b$ is $-1$ .

STEP 5

For the equation $y = \frac{2}{3}x - 2$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $\frac{2}{3}$ . - The y-intercept $b$ is $-2$ .

STEP 6

For the equation $y + 7 = 4x$ :
- Rearrange to slope-intercept form by subtracting 7 from both sides: $ y = 4x - 7 \] - The slope $ m $ is $ 4 $. - The y-intercept $ b $ is $ -7 $.

STEP 7

For the equation $y - 3 = -6x$ :
- Rearrange to slope-intercept form by adding 3 to both sides: $ y = -6x + 3 \] - The slope $ m $ is $ -6 $. - The y-intercept $ b $ is $ 3 $.

STEP 8

For the equation $y + 9 = \frac{3}{4}x$ :
- Rearrange to slope-intercept form by subtracting 9 from both sides: $ y = \frac{3}{4}x - 9 \] - The slope $ m $ is $ \frac{3}{4} $. - The y-intercept $ b $ is $ -9 $.
The slopes and y-intercepts for each equation are:
1. Slope: $3$ , Y-intercept: $4$
2. Slope: $-5$ , Y-intercept: $-1$
3. Slope: $\frac{2}{3}$ , Y-intercept: $-2$
4. Slope: $4$ , Y-intercept: $-7$
5. Slope: $-6$ , Y-intercept: $3$
6. Slope: $\frac{3}{4}$ , Y-intercept: $-9$

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QuestionFind the slope and the $y$ -intercept of the graph of the linear equation.
1. $y=3 x+4$
2. $y=-5 x-1$
3. $y=\frac{2}{3} x-2$
4. $y+7=4 x$
5. $y-3=-6 x$
6. $y+9=\frac{3}{4} x$

Studdy Solution

STEP 1

1. Each equation is in or can be converted to the slope-intercept form of a linear equation, which is $y = mx + b$ .
2. In the slope-intercept form, $m$ represents the slope and $b$ represents the y-intercept.

STEP 2

1. Identify the slope and y-intercept for each equation already in slope-intercept form.
2. Rearrange equations that are not in slope-intercept form to identify the slope and y-intercept.

STEP 3

For the equation $y = 3x + 4$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $3$ . - The y-intercept $b$ is $4$ .

STEP 4

For the equation $y = -5x - 1$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $-5$ . - The y-intercept $b$ is $-1$ .

STEP 5

For the equation $y = \frac{2}{3}x - 2$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $\frac{2}{3}$ . - The y-intercept $b$ is $-2$ .

STEP 6

For the equation $y + 7 = 4x$ :
- Rearrange to slope-intercept form by subtracting 7 from both sides: $ y = 4x - 7 \] - The slope \( m \) is \( 4 \). - The y-intercept \( b \) is \( -7 \).

STEP 7

For the equation $y - 3 = -6x$ :
- Rearrange to slope-intercept form by adding 3 to both sides: $ y = -6x + 3 \] - The slope \( m \) is \( -6 \). - The y-intercept \( b \) is \( 3 \).

STEP 8

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QuestionFind the slope and the yyy-intercept of the graph of the linear equation.1. y=3x+4y=3 x+4y=3x+42. y=−5x−1y=-5 x-1y=−5x−13. y=23x−2y=\frac{2}{3} x-2y=32​x−24. y+7=4xy+7=4 xy+7=4x5. y−3=−6xy-3=-6 xy−3=−6x6. y+9=34xy+9=\frac{3}{4} xy+9=43​x

Studdy Solution

STEP 1

1. Each equation is in or can be converted to the slope-intercept form of a linear equation, which is y=mx+b y = mx + b y=mx+b.2. In the slope-intercept form, m m m represents the slope and b b b represents the y-intercept.

STEP 2

1. Identify the slope and y-intercept for each equation already in slope-intercept form.2. Rearrange equations that are not in slope-intercept form to identify the slope and y-intercept.

STEP 3

For the equation y=3x+4 y = 3x + 4 y=3x+4:- The equation is already in the form y=mx+b y = mx + b y=mx+b. - The slope m m m is 3 3 3. - The y-intercept b b b is 4 4 4.

STEP 4

For the equation y=−5x−1 y = -5x - 1 y=−5x−1:- The equation is already in the form y=mx+b y = mx + b y=mx+b. - The slope m m m is −5 -5 −5. - The y-intercept b b b is −1 -1 −1.

STEP 5

For the equation y=23x−2 y = \frac{2}{3}x - 2 y=32​x−2:- The equation is already in the form y=mx+b y = mx + b y=mx+b. - The slope m m m is 23 \frac{2}{3} 32​. - The y-intercept b b b is −2 -2 −2.

STEP 6

For the equation y+7=4x y + 7 = 4x y+7=4x:- Rearrange to slope-intercept form by subtracting 7 from both sides: $ y = 4x - 7 \] - The slope \( m \) is \( 4 \). - The y-intercept \( b \) is \( -7 \).

STEP 7

For the equation y−3=−6x y - 3 = -6x y−3=−6x:- Rearrange to slope-intercept form by adding 3 to both sides: $ y = -6x + 3 \] - The slope \( m \) is \( -6 \). - The y-intercept \( b \) is \( 3 \).

STEP 8

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Start learning now

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QuestionFind the slope and the $y$ -intercept of the graph of the linear equation.
1. $y=3 x+4$
2. $y=-5 x-1$
3. $y=\frac{2}{3} x-2$
4. $y+7=4 x$
5. $y-3=-6 x$
6. $y+9=\frac{3}{4} x$

1. Each equation is in or can be converted to the slope-intercept form of a linear equation, which is $y = mx + b$ .
2. In the slope-intercept form, $m$ represents the slope and $b$ represents the y-intercept.

1. Identify the slope and y-intercept for each equation already in slope-intercept form.
2. Rearrange equations that are not in slope-intercept form to identify the slope and y-intercept.

For the equation $y = 3x + 4$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $3$ . - The y-intercept $b$ is $4$ .

For the equation $y = -5x - 1$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $-5$ . - The y-intercept $b$ is $-1$ .

For the equation $y = \frac{2}{3}x - 2$ :
- The equation is already in the form $y = mx + b$ . - The slope $m$ is $\frac{2}{3}$ . - The y-intercept $b$ is $-2$ .

For the equation $y + 7 = 4x$ :
- Rearrange to slope-intercept form by subtracting 7 from both sides: $ y = 4x - 7 \] - The slope \( m \) is \( 4 \). - The y-intercept \( b \) is \( -7 \).

For the equation $y - 3 = -6x$ :
- Rearrange to slope-intercept form by adding 3 to both sides: $ y = -6x + 3 \] - The slope \( m \) is \( -6 \). - The y-intercept \( b \) is \( 3 \).