Solved on Jan 22, 2024

Graph the line through points $(-6,-2)$ and $(6,10)$ . Write the line equation $y=mx+b$ .

STEP 1

Assumptions
1. We have two points $(-6,-2)$ and $(6,10)$ .
2. We want to graph the line passing through these points.
3. We want to find the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To graph the line, we will plot the points $(-6,-2)$ and $(6,10)$ on a coordinate plane.

STEP 3

After plotting the points, we will draw a straight line through these points, which will be the graph of the line we are looking for.

STEP 4

To find the equation of the line, we first need to calculate the slope $m$ . The slope is the change in $y$ divided by the change in $x$ between two points on the line.
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 5

Now, plug in the coordinates of the two points into the slope formula.
$m = \frac{10 - (-2)}{6 - (-6)}$

STEP 6

Simplify the numerator and the denominator.
$m = \frac{10 + 2}{6 + 6}$
$m = \frac{12}{12}$

STEP 7

Calculate the slope.
$m = 1$

STEP 8

Now that we have the slope, we need to find the y-intercept $b$ . We can use one of the points and the slope to solve for $b$ using the equation $y = mx + b$ .

STEP 9

Let's use the point $(-6,-2)$ and the slope $m = 1$ to find $b$ .
$-2 = 1 \cdot (-6) + b$

STEP 10

Solve for $b$ .
$-2 = -6 + b$
$b = -2 + 6$

STEP 11

Calculate the value of $b$ .
$b = 4$

STEP 12

Now we have both the slope $m$ and the y-intercept $b$ , so we can write the equation of the line.
$y = mx + b$

STEP 13

Plug in the values for $m$ and $b$ into the equation.
$y = 1x + 4$

STEP 14

Simplify the equation if necessary. In this case, the equation is already simplified.
$y = x + 4$
The equation of the line in the form $y = mx + b$ is $y = x + 4$ .

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Graph the line through points $(-6,-2)$ and $(6,10)$ . Write the line equation $y=mx+b$ .

STEP 1

Assumptions
1. We have two points $(-6,-2)$ and $(6,10)$ .
2. We want to graph the line passing through these points.
3. We want to find the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To graph the line, we will plot the points $(-6,-2)$ and $(6,10)$ on a coordinate plane.

STEP 3

After plotting the points, we will draw a straight line through these points, which will be the graph of the line we are looking for.

STEP 4

To find the equation of the line, we first need to calculate the slope $m$ . The slope is the change in $y$ divided by the change in $x$ between two points on the line.
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 5

Now, plug in the coordinates of the two points into the slope formula.
$m = \frac{10 - (-2)}{6 - (-6)}$

STEP 6

Simplify the numerator and the denominator.
$m = \frac{10 + 2}{6 + 6}$
$m = \frac{12}{12}$

STEP 7

Calculate the slope.
$m = 1$

STEP 8

Now that we have the slope, we need to find the y-intercept $b$ . We can use one of the points and the slope to solve for $b$ using the equation $y = mx + b$ .

STEP 9

Let's use the point $(-6,-2)$ and the slope $m = 1$ to find $b$ .
$-2 = 1 \cdot (-6) + b$

STEP 10

Solve for $b$ .
$-2 = -6 + b$
$b = -2 + 6$

STEP 11

Calculate the value of $b$ .
$b = 4$

STEP 12

Now we have both the slope $m$ and the y-intercept $b$ , so we can write the equation of the line.
$y = mx + b$

STEP 13

Plug in the values for $m$ and $b$ into the equation.
$y = 1x + 4$

STEP 14

Simplify the equation if necessary. In this case, the equation is already simplified.
$y = x + 4$
The equation of the line in the form $y = mx + b$ is $y = x + 4$ .

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Graph the line through points (−6,−2)(-6,-2)(−6,−2) and (6,10)(6,10)(6,10). Write the line equation y=mx+by=mx+by=mx+b.

STEP 1

Assumptions1. We have two points (−6,−2)(-6,-2)(−6,−2) and (6,10)(6,10)(6,10).2. We want to graph the line passing through these points.3. We want to find the equation of the line in the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

To graph the line, we will plot the points (−6,−2)(-6,-2)(−6,−2) and (6,10)(6,10)(6,10) on a coordinate plane.

STEP 3

After plotting the points, we will draw a straight line through these points, which will be the graph of the line we are looking for.

STEP 4

To find the equation of the line, we first need to calculate the slope mmm. The slope is the change in yyy divided by the change in xxx between two points on the line.m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​

STEP 5

Now, plug in the coordinates of the two points into the slope formula.m=10−(−2)6−(−6)m = \frac{10 - (-2)}{6 - (-6)}m=6−(−6)10−(−2)​

STEP 6

Simplify the numerator and the denominator.m=10+26+6m = \frac{10 + 2}{6 + 6}m=6+610+2​m=1212m = \frac{12}{12}m=1212​

STEP 7

Calculate the slope.m=1m = 1m=1

STEP 8

Now that we have the slope, we need to find the y-intercept bbb. We can use one of the points and the slope to solve for bbb using the equation y=mx+by = mx + by=mx+b.

STEP 9

Let's use the point (−6,−2)(-6,-2)(−6,−2) and the slope m=1m = 1m=1 to find bbb.−2=1⋅(−6)+b-2 = 1 \cdot (-6) + b−2=1⋅(−6)+b

STEP 10

Solve for bbb.−2=−6+b-2 = -6 + b−2=−6+bb=−2+6b = -2 + 6b=−2+6

STEP 11

Calculate the value of bbb.b=4b = 4b=4

STEP 12

Now we have both the slope mmm and the y-intercept bbb, so we can write the equation of the line.y=mx+by = mx + by=mx+b

STEP 13

Plug in the values for mmm and bbb into the equation.y=1x+4y = 1x + 4y=1x+4

STEP 14

Simplify the equation if necessary. In this case, the equation is already simplified.y=x+4y = x + 4y=x+4The equation of the line in the form y=mx+by = mx + by=mx+b is y=x+4y = x + 4y=x+4.

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

Graph the line through points $(-6,-2)$ and $(6,10)$ . Write the line equation $y=mx+b$ .

Assumptions
1. We have two points $(-6,-2)$ and $(6,10)$ .
2. We want to graph the line passing through these points.
3. We want to find the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

To graph the line, we will plot the points $(-6,-2)$ and $(6,10)$ on a coordinate plane.

To find the equation of the line, we first need to calculate the slope $m$ . The slope is the change in $y$ divided by the change in $x$ between two points on the line.
$m = \frac{y_2 - y_1}{x_2 - x_1}$

Now, plug in the coordinates of the two points into the slope formula.
$m = \frac{10 - (-2)}{6 - (-6)}$

Simplify the numerator and the denominator.
$m = \frac{10 + 2}{6 + 6}$
$m = \frac{12}{12}$

Calculate the slope.
$m = 1$

Now that we have the slope, we need to find the y-intercept $b$ . We can use one of the points and the slope to solve for $b$ using the equation $y = mx + b$ .

Let's use the point $(-6,-2)$ and the slope $m = 1$ to find $b$ .
$-2 = 1 \cdot (-6) + b$

Solve for $b$ .
$-2 = -6 + b$
$b = -2 + 6$

Calculate the value of $b$ .
$b = 4$

Now we have both the slope $m$ and the y-intercept $b$ , so we can write the equation of the line.
$y = mx + b$

Plug in the values for $m$ and $b$ into the equation.
$y = 1x + 4$

Simplify the equation if necessary. In this case, the equation is already simplified.
$y = x + 4$
The equation of the line in the form $y = mx + b$ is $y = x + 4$ .