QuestionFind the line equation through points (1,2) and (5,10). Use $y = mx + b$ to determine $m$ and $b$ .

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian coordinate system $(1,)$ and $(5,10)$ . . We are looking for the equation of a line in the form $y = mx + c$ , where $m$ is the slope of the line 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 $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for the points into the slope formula.
$m = \frac{10 -2}{5 -1}$

STEP 4

Calculate the slope.
$m = \frac{8}{4} =2$

STEP 5

Now that we have the slope, we can find the y-intercept $c$ by rearranging the equation of the line and substituting one of the points and the slope into the equation.
$c = y - mx$

STEP 6

Substitute the point $(1,2)$ and the slope $m=2$ into the equation to find the y-intercept.
$c =2 -2 \times1$

STEP 7

Calculate the y-intercept.
$c =2 -2 =0$

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + c$

STEP 9

Substitute the values of $m$ and $c$ into the equation.
$y =2x +$

STEP 10

implify the equation.
$y =2x$ The equation of the line passing through the points $(,2)$ and $(5,10)$ is $y =2x$ .

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QuestionFind the line equation through points (1,2) and (5,10). Use $y = mx + b$ to determine $m$ and $b$ .

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian coordinate system $(1,)$ and $(5,10)$ . . We are looking for the equation of a line in the form $y = mx + c$ , where $m$ is the slope of the line 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 $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for the points into the slope formula.
$m = \frac{10 -2}{5 -1}$

STEP 4

Calculate the slope.
$m = \frac{8}{4} =2$

STEP 5

Now that we have the slope, we can find the y-intercept $c$ by rearranging the equation of the line and substituting one of the points and the slope into the equation.
$c = y - mx$

STEP 6

Substitute the point $(1,2)$ and the slope $m=2$ into the equation to find the y-intercept.
$c =2 -2 \times1$

STEP 7

Calculate the y-intercept.
$c =2 -2 =0$

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + c$

STEP 9

Substitute the values of $m$ and $c$ into the equation.
$y =2x +$

STEP 10

implify the equation.
$y =2x$ The equation of the line passing through the points $(,2)$ and $(5,10)$ is $y =2x$ .

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QuestionFind the line equation through points (1,2) and (5,10). Use y=mx+by = mx + by=mx+b to determine mmm and bbb.

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian coordinate system (1,)(1,)(1,) and (5,10)(5,10)(5,10). . We are looking for the equation of a line in the form y=mx+cy = mx + cy=mx+c, where mmm is the slope of the line and ccc is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Now, plug in the given values for the points into the slope formula.m=10−25−1m = \frac{10 -2}{5 -1}m=5−110−2​

STEP 4

Calculate the slope.m=84=2m = \frac{8}{4} =2m=48​=2

STEP 5

Now that we have the slope, we can find the y-intercept ccc by rearranging the equation of the line and substituting one of the points and the slope into the equation.c=y−mxc = y - mxc=y−mx

STEP 6

Substitute the point (1,2)(1,2)(1,2) and the slope m=2m=2m=2 into the equation to find the y-intercept.c=2−2×1c =2 -2 \times1c=2−2×1

STEP 7

Calculate the y-intercept.c=2−2=0c =2 -2 =0c=2−2=0

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.y=mx+cy = mx + cy=mx+c

STEP 9

Substitute the values of mmm and ccc into the equation.y=2x+y =2x +y=2x+

STEP 10

implify the equation.y=2xy =2xy=2xThe equation of the line passing through the points (,2)(,2)(,2) and (5,10)(5,10)(5,10) is y=2xy =2xy=2x.

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QuestionFind the line equation through points (1,2) and (5,10). Use $y = mx + b$ to determine $m$ and $b$ .

Assumptions1. We have two points in the Cartesian coordinate system $(1,)$ and $(5,10)$ . . We are looking for the equation of a line in the form $y = mx + c$ , where $m$ is the slope of the line and $c$ is the y-intercept.

First, we need to find the slope of the line. The slope is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for the points into the slope formula.
$m = \frac{10 -2}{5 -1}$

Calculate the slope.
$m = \frac{8}{4} =2$

Now that we have the slope, we can find the y-intercept $c$ by rearranging the equation of the line and substituting one of the points and the slope into the equation.
$c = y - mx$

Substitute the point $(1,2)$ and the slope $m=2$ into the equation to find the y-intercept.
$c =2 -2 \times1$

Calculate the y-intercept.
$c =2 -2 =0$

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + c$

Substitute the values of $m$ and $c$ into the equation.
$y =2x +$

implify the equation.
$y =2x$ The equation of the line passing through the points $(,2)$ and $(5,10)$ is $y =2x$ .