Math / Geometry

Question25. What must be known to graph the equation $6 x+8 y=480$ on a coordinate plane? a. The maximum values for $x$ and $y$ only b. The differential of $x$ and $y$ c. The intercepts where the line crosses the axes d. The derivatives of $x$ and $y$

Studdy Solution

STEP 1

1. The equation to be graphed is a linear equation in the form $Ax + By = C$ .
2. To graph a linear equation, it is helpful to determine the points where the line crosses the x-axis and y-axis, known as the intercepts.

STEP 2

1. Rewrite the given equation in slope-intercept form if necessary.
2. Calculate the x-intercept by setting $y=0$ and solving for $x$ .
3. Calculate the y-intercept by setting $x=0$ and solving for $y$ .
4. Use the intercepts to plot the line on a coordinate plane.

STEP 3

Rewrite the equation $6x + 8y = 480$ in slope-intercept form ( $y = mx + b$ ) if needed.
$6x + 8y = 480$

STEP 4

Solve for $y$ to put the equation in slope-intercept form.
$8y = -6x + 480$ $y = -\frac{6}{8}x + \frac{480}{8}$ $y = -\frac{3}{4}x + 60$

STEP 5

Calculate the x-intercept by setting $y = 0$ and solving for $x$ .
$6x + 8(0) = 480$ $6x = 480$ $x = \frac{480}{6}$ $x = 80$

STEP 6

Calculate the y-intercept by setting $x = 0$ and solving for $y$ .
$6(0) + 8y = 480$ $8y = 480$ $y = \frac{480}{8}$ $y = 60$

STEP 7

Plot the intercepts on the coordinate plane: the x-intercept at $(80, 0)$ and the y-intercept at $(0, 60)$ . Draw the line that passes through these intercepts to graph the equation $6x + 8y = 480$ .
The correct answer to the problem is: c. The intercepts where the line crosses the axes

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Question25. What must be known to graph the equation $6 x+8 y=480$ on a coordinate plane? a. The maximum values for $x$ and $y$ only b. The differential of $x$ and $y$ c. The intercepts where the line crosses the axes d. The derivatives of $x$ and $y$

Studdy Solution

STEP 1

1. The equation to be graphed is a linear equation in the form $Ax + By = C$ .
2. To graph a linear equation, it is helpful to determine the points where the line crosses the x-axis and y-axis, known as the intercepts.

STEP 2

1. Rewrite the given equation in slope-intercept form if necessary.
2. Calculate the x-intercept by setting $y=0$ and solving for $x$ .
3. Calculate the y-intercept by setting $x=0$ and solving for $y$ .
4. Use the intercepts to plot the line on a coordinate plane.

STEP 3

Rewrite the equation $6x + 8y = 480$ in slope-intercept form ( $y = mx + b$ ) if needed.
$6x + 8y = 480$

STEP 4

Solve for $y$ to put the equation in slope-intercept form.
$8y = -6x + 480$ $y = -\frac{6}{8}x + \frac{480}{8}$ $y = -\frac{3}{4}x + 60$

STEP 5

Calculate the x-intercept by setting $y = 0$ and solving for $x$ .
$6x + 8(0) = 480$ $6x = 480$ $x = \frac{480}{6}$ $x = 80$

STEP 6

Calculate the y-intercept by setting $x = 0$ and solving for $y$ .
$6(0) + 8y = 480$ $8y = 480$ $y = \frac{480}{8}$ $y = 60$

STEP 7

Plot the intercepts on the coordinate plane: the x-intercept at $(80, 0)$ and the y-intercept at $(0, 60)$ . Draw the line that passes through these intercepts to graph the equation $6x + 8y = 480$ .
The correct answer to the problem is: c. The intercepts where the line crosses the axes

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Question25. What must be known to graph the equation 6x+8y=4806 x+8 y=4806x+8y=480 on a coordinate plane? a. The maximum values for xxx and yyy only b. The differential of xxx and yyy c. The intercepts where the line crosses the axes d. The derivatives of xxx and yyy

Studdy Solution

STEP 1

1. The equation to be graphed is a linear equation in the form Ax+By=CAx + By = CAx+By=C.2. To graph a linear equation, it is helpful to determine the points where the line crosses the x-axis and y-axis, known as the intercepts.

STEP 2

1. Rewrite the given equation in slope-intercept form if necessary.2. Calculate the x-intercept by setting y=0y=0y=0 and solving for xxx.3. Calculate the y-intercept by setting x=0x=0x=0 and solving for yyy.4. Use the intercepts to plot the line on a coordinate plane.

STEP 3

Rewrite the equation 6x+8y=4806x + 8y = 4806x+8y=480 in slope-intercept form (y=mx+by = mx + by=mx+b) if needed.6x+8y=4806x + 8y = 4806x+8y=480

STEP 4

Solve for yyy to put the equation in slope-intercept form.8y=−6x+4808y = -6x + 4808y=−6x+480 y=−68x+4808y = -\frac{6}{8}x + \frac{480}{8}y=−86​x+8480​ y=−34x+60y = -\frac{3}{4}x + 60y=−43​x+60

STEP 5

Calculate the x-intercept by setting y=0y = 0y=0 and solving for xxx.6x+8(0)=4806x + 8(0) = 4806x+8(0)=480 6x=4806x = 4806x=480 x=4806x = \frac{480}{6}x=6480​ x=80x = 80x=80

STEP 6

Calculate the y-intercept by setting x=0x = 0x=0 and solving for yyy.6(0)+8y=4806(0) + 8y = 4806(0)+8y=480 8y=4808y = 4808y=480 y=4808y = \frac{480}{8}y=8480​ y=60y = 60y=60

STEP 7

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Question25. What must be known to graph the equation $6 x+8 y=480$ on a coordinate plane? a. The maximum values for $x$ and $y$ only b. The differential of $x$ and $y$ c. The intercepts where the line crosses the axes d. The derivatives of $x$ and $y$

1. The equation to be graphed is a linear equation in the form $Ax + By = C$ .
2. To graph a linear equation, it is helpful to determine the points where the line crosses the x-axis and y-axis, known as the intercepts.

1. Rewrite the given equation in slope-intercept form if necessary.
2. Calculate the x-intercept by setting $y=0$ and solving for $x$ .
3. Calculate the y-intercept by setting $x=0$ and solving for $y$ .
4. Use the intercepts to plot the line on a coordinate plane.

Rewrite the equation $6x + 8y = 480$ in slope-intercept form ( $y = mx + b$ ) if needed.
$6x + 8y = 480$

Solve for $y$ to put the equation in slope-intercept form.
$8y = -6x + 480$ $y = -\frac{6}{8}x + \frac{480}{8}$ $y = -\frac{3}{4}x + 60$

Calculate the x-intercept by setting $y = 0$ and solving for $x$ .
$6x + 8(0) = 480$ $6x = 480$ $x = \frac{480}{6}$ $x = 80$

Calculate the y-intercept by setting $x = 0$ and solving for $y$ .
$6(0) + 8y = 480$ $8y = 480$ $y = \frac{480}{8}$ $y = 60$