Question Find the equation of the line passing through (3,10) and (7,28) in the form $y=mx+c$ , where $m$ and $c$ are integers or simplified fractions.

Studdy Solution

STEP 1

Assumptions
1. The line passes through the points $(3,10)$ and $(7,28)$ .
2. The equation of a straight line is in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 3

Now, plug in the given values for $x_1$ , $y_1$ , $x_2$ , and $y_2$ to calculate the slope.
$m = \frac{28 - 10}{7 - 3}$

STEP 4

Calculate the slope.
$m = \frac{18}{4} = \frac{9}{2}$

STEP 5

Now that we have the slope, we can find the y-intercept $c$ . We can use the equation of the line and one of the points to solve for $c$ . Let's use the point $(3,10)$ .
$10 = \frac{9}{2} \cdot 3 + c$

STEP 6

Solve the equation for $c$ .
$c = 10 - \frac{9}{2} \cdot 3$

STEP 7

Calculate the y-intercept.
$c = 10 - \frac{27}{2} = -\frac{7}{2}$

STEP 8

Now that we have both the slope $m$ and the y-intercept $c$ , we can write the equation of the line.
$y = \frac{9}{2}x - \frac{7}{2}$
The equation of the line that passes through $(3,10)$ and $(7,28)$ is $y = \frac{9}{2}x - \frac{7}{2}$ .

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Question Find the equation of the line passing through (3,10) and (7,28) in the form $y=mx+c$ , where $m$ and $c$ are integers or simplified fractions.

Studdy Solution

STEP 1

Assumptions
1. The line passes through the points $(3,10)$ and $(7,28)$ .
2. The equation of a straight line is in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 3

Now, plug in the given values for $x_1$ , $y_1$ , $x_2$ , and $y_2$ to calculate the slope.
$m = \frac{28 - 10}{7 - 3}$

STEP 4

Calculate the slope.
$m = \frac{18}{4} = \frac{9}{2}$

STEP 5

Now that we have the slope, we can find the y-intercept $c$ . We can use the equation of the line and one of the points to solve for $c$ . Let's use the point $(3,10)$ .
$10 = \frac{9}{2} \cdot 3 + c$

STEP 6

Solve the equation for $c$ .
$c = 10 - \frac{9}{2} \cdot 3$

STEP 7

Calculate the y-intercept.
$c = 10 - \frac{27}{2} = -\frac{7}{2}$

STEP 8

Now that we have both the slope $m$ and the y-intercept $c$ , we can write the equation of the line.
$y = \frac{9}{2}x - \frac{7}{2}$
The equation of the line that passes through $(3,10)$ and $(7,28)$ is $y = \frac{9}{2}x - \frac{7}{2}$ .

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Question Find the equation of the line passing through (3,10) and (7,28) in the form y=mx+cy=mx+cy=mx+c, where mmm and ccc are integers or simplified fractions.

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (3,10)(3,10)(3,10) and (7,28)(7,28)(7,28).2. The equation of a straight line is in the form y=mx+cy = mx + cy=mx+c, where mmm is the slope and ccc is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formula:m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​

STEP 3

Now, plug in the given values for x1x_1x1​, y1y_1y1​, x2x_2x2​, and y2y_2y2​ to calculate the slope.m=28−107−3m = \frac{28 - 10}{7 - 3}m=7−328−10​

STEP 4

Calculate the slope.m=184=92m = \frac{18}{4} = \frac{9}{2}m=418​=29​

STEP 5

Now that we have the slope, we can find the y-intercept ccc. We can use the equation of the line and one of the points to solve for ccc. Let's use the point (3,10)(3,10)(3,10).10=92⋅3+c10 = \frac{9}{2} \cdot 3 + c10=29​⋅3+c

STEP 6

Solve the equation for ccc.c=10−92⋅3c = 10 - \frac{9}{2} \cdot 3c=10−29​⋅3

STEP 7

Calculate the y-intercept.c=10−272=−72c = 10 - \frac{27}{2} = -\frac{7}{2}c=10−227​=−27​

STEP 8

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Question Find the equation of the line passing through (3,10) and (7,28) in the form $y=mx+c$ , where $m$ and $c$ are integers or simplified fractions.

Assumptions
1. The line passes through the points $(3,10)$ and $(7,28)$ .
2. The equation of a straight line is in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

First, we need to find the slope of the line. The slope is given by the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

Now, plug in the given values for $x_1$ , $y_1$ , $x_2$ , and $y_2$ to calculate the slope.
$m = \frac{28 - 10}{7 - 3}$

Calculate the slope.
$m = \frac{18}{4} = \frac{9}{2}$

Now that we have the slope, we can find the y-intercept $c$ . We can use the equation of the line and one of the points to solve for $c$ . Let's use the point $(3,10)$ .
$10 = \frac{9}{2} \cdot 3 + c$

Solve the equation for $c$ .
$c = 10 - \frac{9}{2} \cdot 3$

Calculate the y-intercept.
$c = 10 - \frac{27}{2} = -\frac{7}{2}$