Math / Algebra

QuestionThe alope of any hertiwontits line is the came he than of dhe line has the form $y=$ bl. Wertick because their slope is underinch, best fhe form $x$ . The equation of a vertical lime the $x$ -intercepl. A. Exercises
9. $y=2 x+3$
1. $x+y=2$
5. $4 x+2 y=12$ equation.
4. $2 x-y=3$
Use the $y$ -intercept and slope to graph s. $y=3 x$
8. point. Then write the equation of
7. $y=x-5$
11. $x+3 y=12$
10. $3 x+y=1$

Studdy Solution

STEP 1

1. We need to graph linear equations using the $y$ -intercept and slope.
2. We will identify the slope and $y$ -intercept from the given equations.
3. We will use the slope-intercept form $y = mx + b$ where $m$ is the slope and $b$ is the $y$ -intercept.
4. The task involves graphing and writing equations of lines.

STEP 2

1. Identify the slope and $y$ -intercept from each equation.
2. Graph the equation using the slope and $y$ -intercept.
3. Write the equation of a line given a point and a slope.

STEP 3

For the equation $y = 2x + 3$ , identify the slope and $y$ -intercept: - Slope ( $m$ ) = 2 - $y$ -intercept ( $b$ ) = 3

STEP 4

For the equation $x + y = 2$ , rewrite it in slope-intercept form: - Rearrange to $y = -x + 2$ - Slope ( $m$ ) = -1 - $y$ -intercept ( $b$ ) = 2

STEP 5

For the equation $4x + 2y = 12$ , rewrite it in slope-intercept form: - Rearrange to $2y = -4x + 12$ - Simplify to $y = -2x + 6$ - Slope ( $m$ ) = -2 - $y$ -intercept ( $b$ ) = 6

STEP 6

For the equation $2x - y = 3$ , rewrite it in slope-intercept form: - Rearrange to $y = 2x - 3$ - Slope ( $m$ ) = 2 - $y$ -intercept ( $b$ ) = -3

STEP 7

Graph each equation using the identified slope and $y$ -intercept: - Start at the $y$ -intercept on the graph. - Use the slope to determine the rise over run and plot the next point. - Draw the line through the points.

STEP 8

Write the equation of a line given a point and a slope: - Use the point-slope form $y - y_1 = m(x - x_1)$ . - Rearrange to slope-intercept form if needed.
The steps above outline how to graph linear equations and write equations of lines given specific conditions.

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Studdy Solution

STEP 1

STEP 2

1. Identify the slope and $y$ -intercept from each equation.
2. Graph the equation using the slope and $y$ -intercept.
3. Write the equation of a line given a point and a slope.

STEP 3

For the equation $y = 2x + 3$ , identify the slope and $y$ -intercept: - Slope ( $m$ ) = 2 - $y$ -intercept ( $b$ ) = 3

STEP 4

For the equation $x + y = 2$ , rewrite it in slope-intercept form: - Rearrange to $y = -x + 2$ - Slope ( $m$ ) = -1 - $y$ -intercept ( $b$ ) = 2

STEP 5

For the equation $4x + 2y = 12$ , rewrite it in slope-intercept form: - Rearrange to $2y = -4x + 12$ - Simplify to $y = -2x + 6$ - Slope ( $m$ ) = -2 - $y$ -intercept ( $b$ ) = 6

STEP 6

For the equation $2x - y = 3$ , rewrite it in slope-intercept form: - Rearrange to $y = 2x - 3$ - Slope ( $m$ ) = 2 - $y$ -intercept ( $b$ ) = -3

STEP 7

Graph each equation using the identified slope and $y$ -intercept: - Start at the $y$ -intercept on the graph. - Use the slope to determine the rise over run and plot the next point. - Draw the line through the points.

STEP 8

Write the equation of a line given a point and a slope: - Use the point-slope form $y - y_1 = m(x - x_1)$ . - Rearrange to slope-intercept form if needed.
The steps above outline how to graph linear equations and write equations of lines given specific conditions.

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Studdy Solution

STEP 1

STEP 2

1. Identify the slope and y y y-intercept from each equation.2. Graph the equation using the slope and y y y-intercept.3. Write the equation of a line given a point and a slope.

STEP 3

For the equation y=2x+3 y = 2x + 3 y=2x+3, identify the slope and y y y-intercept: - Slope (m m m) = 2 - y y y-intercept (b b b) = 3

STEP 4

For the equation x+y=2 x + y = 2 x+y=2, rewrite it in slope-intercept form: - Rearrange to y=−x+2 y = -x + 2 y=−x+2 - Slope (m m m) = -1 - y y y-intercept (b b b) = 2

STEP 5

For the equation 4x+2y=12 4x + 2y = 12 4x+2y=12, rewrite it in slope-intercept form: - Rearrange to 2y=−4x+12 2y = -4x + 12 2y=−4x+12 - Simplify to y=−2x+6 y = -2x + 6 y=−2x+6 - Slope (m m m) = -2 - y y y-intercept (b b b) = 6

STEP 6

For the equation 2x−y=3 2x - y = 3 2x−y=3, rewrite it in slope-intercept form: - Rearrange to y=2x−3 y = 2x - 3 y=2x−3 - Slope (m m m) = 2 - y y y-intercept (b b b) = -3

STEP 7

Graph each equation using the identified slope and y y y-intercept: - Start at the y y y-intercept on the graph. - Use the slope to determine the rise over run and plot the next point. - Draw the line through the points.

STEP 8

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1. Identify the slope and $y$ -intercept from each equation.
2. Graph the equation using the slope and $y$ -intercept.
3. Write the equation of a line given a point and a slope.

For the equation $y = 2x + 3$ , identify the slope and $y$ -intercept: - Slope ( $m$ ) = 2 - $y$ -intercept ( $b$ ) = 3

For the equation $x + y = 2$ , rewrite it in slope-intercept form: - Rearrange to $y = -x + 2$ - Slope ( $m$ ) = -1 - $y$ -intercept ( $b$ ) = 2

For the equation $4x + 2y = 12$ , rewrite it in slope-intercept form: - Rearrange to $2y = -4x + 12$ - Simplify to $y = -2x + 6$ - Slope ( $m$ ) = -2 - $y$ -intercept ( $b$ ) = 6

For the equation $2x - y = 3$ , rewrite it in slope-intercept form: - Rearrange to $y = 2x - 3$ - Slope ( $m$ ) = 2 - $y$ -intercept ( $b$ ) = -3

Graph each equation using the identified slope and $y$ -intercept: - Start at the $y$ -intercept on the graph. - Use the slope to determine the rise over run and plot the next point. - Draw the line through the points.