Math / Algebra

Question $\begin{array}{c} y=-\frac{1}{2} x+4 \\ y=2 x-1 \end{array}$
Plot two lines by clicking the graph. Click a line to delete it.

Studdy Solution

STEP 1

1. We have a system of two linear equations that we need to plot on a graph.
2. The equations are given in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
3. The task involves plotting these lines on a coordinate plane.

STEP 2

1. Identify the slope and y-intercept for each equation.
2. Plot the y-intercept for each line on the graph.
3. Use the slope to determine another point for each line.
4. Draw the lines through the points.
5. Check the intersection of the lines, if any.

STEP 3

For the first equation $y = -\frac{1}{2}x + 4$ : - The slope ( $m$ ) is $-\frac{1}{2}$ . - The y-intercept ( $b$ ) is $4$ .
For the second equation $y = 2x - 1$ : - The slope ( $m$ ) is $2$ . - The y-intercept ( $b$ ) is $-1$ .

STEP 4

Plot the y-intercept of the first line: - Start at the point $(0, 4)$ on the y-axis.
Plot the y-intercept of the second line: - Start at the point $(0, -1)$ on the y-axis.

STEP 5

For the first line $y = -\frac{1}{2}x + 4$ : - From the y-intercept $(0, 4)$ , use the slope $-\frac{1}{2}$ to find another point. - Move down 1 unit and right 2 units to the point $(2, 3)$ .
For the second line $y = 2x - 1$ : - From the y-intercept $(0, -1)$ , use the slope $2$ to find another point. - Move up 2 units and right 1 unit to the point $(1, 1)$ .

STEP 6

Draw the first line through the points $(0, 4)$ and $(2, 3)$ .
Draw the second line through the points $(0, -1)$ and $(1, 1)$ .

STEP 7

Check the intersection of the lines: - The lines intersect at the point where both equations are satisfied. - Solve the system of equations to find the intersection point, if necessary.

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Question $\begin{array}{c} y=-\frac{1}{2} x+4 \\ y=2 x-1 \end{array}$
Plot two lines by clicking the graph. Click a line to delete it.

Studdy Solution

STEP 1

1. We have a system of two linear equations that we need to plot on a graph.
2. The equations are given in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
3. The task involves plotting these lines on a coordinate plane.

STEP 2

1. Identify the slope and y-intercept for each equation.
2. Plot the y-intercept for each line on the graph.
3. Use the slope to determine another point for each line.
4. Draw the lines through the points.
5. Check the intersection of the lines, if any.

STEP 3

For the first equation $y = -\frac{1}{2}x + 4$ : - The slope ( $m$ ) is $-\frac{1}{2}$ . - The y-intercept ( $b$ ) is $4$ .
For the second equation $y = 2x - 1$ : - The slope ( $m$ ) is $2$ . - The y-intercept ( $b$ ) is $-1$ .

STEP 4

Plot the y-intercept of the first line: - Start at the point $(0, 4)$ on the y-axis.
Plot the y-intercept of the second line: - Start at the point $(0, -1)$ on the y-axis.

STEP 5

STEP 6

Draw the first line through the points $(0, 4)$ and $(2, 3)$ .
Draw the second line through the points $(0, -1)$ and $(1, 1)$ .

STEP 7

Check the intersection of the lines: - The lines intersect at the point where both equations are satisfied. - Solve the system of equations to find the intersection point, if necessary.

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Questiony=−12x+4y=2x−1\begin{array}{c} y=-\frac{1}{2} x+4 \\ y=2 x-1 \end{array}y=−21​x+4y=2x−1​Plot two lines by clicking the graph. Click a line to delete it.

Studdy Solution

STEP 1

1. We have a system of two linear equations that we need to plot on a graph.2. The equations are given in slope-intercept form, y=mx+b y = mx + b y=mx+b, where m m m is the slope and b b b is the y-intercept.3. The task involves plotting these lines on a coordinate plane.

STEP 2

1. Identify the slope and y-intercept for each equation.2. Plot the y-intercept for each line on the graph.3. Use the slope to determine another point for each line.4. Draw the lines through the points.5. Check the intersection of the lines, if any.

STEP 3

For the first equation y=−12x+4 y = -\frac{1}{2}x + 4 y=−21​x+4: - The slope (m m m) is −12 -\frac{1}{2} −21​. - The y-intercept (b b b) is 4 4 4.For the second equation y=2x−1 y = 2x - 1 y=2x−1: - The slope (m m m) is 2 2 2. - The y-intercept (b b b) is −1 -1 −1.

STEP 4

Plot the y-intercept of the first line: - Start at the point (0,4) (0, 4) (0,4) on the y-axis.Plot the y-intercept of the second line: - Start at the point (0,−1) (0, -1) (0,−1) on the y-axis.

STEP 5

STEP 6

Draw the first line through the points (0,4) (0, 4) (0,4) and (2,3) (2, 3) (2,3).Draw the second line through the points (0,−1) (0, -1) (0,−1) and (1,1) (1, 1) (1,1).

STEP 7

Check the intersection of the lines: - The lines intersect at the point where both equations are satisfied. - Solve the system of equations to find the intersection point, if necessary.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\begin{array}{c} y=-\frac{1}{2} x+4 \\ y=2 x-1 \end{array}$
Plot two lines by clicking the graph. Click a line to delete it.

1. We have a system of two linear equations that we need to plot on a graph.
2. The equations are given in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
3. The task involves plotting these lines on a coordinate plane.

1. Identify the slope and y-intercept for each equation.
2. Plot the y-intercept for each line on the graph.
3. Use the slope to determine another point for each line.
4. Draw the lines through the points.
5. Check the intersection of the lines, if any.

For the first equation $y = -\frac{1}{2}x + 4$ : - The slope ( $m$ ) is $-\frac{1}{2}$ . - The y-intercept ( $b$ ) is $4$ .
For the second equation $y = 2x - 1$ : - The slope ( $m$ ) is $2$ . - The y-intercept ( $b$ ) is $-1$ .

Plot the y-intercept of the first line: - Start at the point $(0, 4)$ on the y-axis.
Plot the y-intercept of the second line: - Start at the point $(0, -1)$ on the y-axis.

Draw the first line through the points $(0, 4)$ and $(2, 3)$ .
Draw the second line through the points $(0, -1)$ and $(1, 1)$ .