Solved on Jan 22, 2024

Find the equation $y=mx$ for the proportional relationship passing through the points $(2,-15)$ and $(6,-45)$ .

STEP 1

Assumptions
1. The relationship between $x$ and $y$ is proportional, which means it can be described by an equation of the form $y = mx$ , where $m$ is the constant of proportionality.
2. The line passes through the points $(2, -15)$ and $(6, -45)$ .

STEP 2

To find the constant of proportionality $m$ , we can use the two given points. The constant $m$ is the ratio of the change in $y$ to the change in $x$ .
$m = \frac{\Delta y}{\Delta x}$

STEP 3

Calculate the change in $y$ ( $\Delta y$ ) using the $y$ -coordinates of the given points.
$\Delta y = y_2 - y_1$

STEP 4

Substitute the $y$ -coordinates of the points into the formula.
$\Delta y = -45 - (-15)$

STEP 5

Calculate the change in $y$ .
$\Delta y = -45 + 15 = -30$

STEP 6

Calculate the change in $x$ ( $\Delta x$ ) using the $x$ -coordinates of the given points.
$\Delta x = x_2 - x_1$

STEP 7

Substitute the $x$ -coordinates of the points into the formula.
$\Delta x = 6 - 2$

STEP 8

Calculate the change in $x$ .
$\Delta x = 6 - 2 = 4$

STEP 9

Now, calculate the constant of proportionality $m$ using the changes in $y$ and $x$ .
$m = \frac{\Delta y}{\Delta x}$

STEP 10

Substitute the values for $\Delta y$ and $\Delta x$ into the formula.
$m = \frac{-30}{4}$

STEP 11

Calculate the constant of proportionality $m$ .
$m = \frac{-30}{4} = -7.5$

STEP 12

Now that we have the constant of proportionality $m$ , we can write the equation of the proportional relationship.
$y = mx$

STEP 13

Substitute the value of $m$ into the equation.
$y = -7.5x$
The equation for the proportional relationship that passes through the points $(2,-15)$ and $(6,-45)$ is $y = -7.5x$ .

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Find the equation $y=mx$ for the proportional relationship passing through the points $(2,-15)$ and $(6,-45)$ .

STEP 1

Assumptions
1. The relationship between $x$ and $y$ is proportional, which means it can be described by an equation of the form $y = mx$ , where $m$ is the constant of proportionality.
2. The line passes through the points $(2, -15)$ and $(6, -45)$ .

STEP 2

To find the constant of proportionality $m$ , we can use the two given points. The constant $m$ is the ratio of the change in $y$ to the change in $x$ .
$m = \frac{\Delta y}{\Delta x}$

STEP 3

Calculate the change in $y$ ( $\Delta y$ ) using the $y$ -coordinates of the given points.
$\Delta y = y_2 - y_1$

STEP 4

Substitute the $y$ -coordinates of the points into the formula.
$\Delta y = -45 - (-15)$

STEP 5

Calculate the change in $y$ .
$\Delta y = -45 + 15 = -30$

STEP 6

Calculate the change in $x$ ( $\Delta x$ ) using the $x$ -coordinates of the given points.
$\Delta x = x_2 - x_1$

STEP 7

Substitute the $x$ -coordinates of the points into the formula.
$\Delta x = 6 - 2$

STEP 8

Calculate the change in $x$ .
$\Delta x = 6 - 2 = 4$

STEP 9

Now, calculate the constant of proportionality $m$ using the changes in $y$ and $x$ .
$m = \frac{\Delta y}{\Delta x}$

STEP 10

Substitute the values for $\Delta y$ and $\Delta x$ into the formula.
$m = \frac{-30}{4}$

STEP 11

Calculate the constant of proportionality $m$ .
$m = \frac{-30}{4} = -7.5$

STEP 12

Now that we have the constant of proportionality $m$ , we can write the equation of the proportional relationship.
$y = mx$

STEP 13

Substitute the value of $m$ into the equation.
$y = -7.5x$
The equation for the proportional relationship that passes through the points $(2,-15)$ and $(6,-45)$ is $y = -7.5x$ .

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Find the equation y=mxy=mxy=mx for the proportional relationship passing through the points (2,−15)(2,-15)(2,−15) and (6,−45)(6,-45)(6,−45).

STEP 1

Assumptions1. The relationship between xxx and yyy is proportional, which means it can be described by an equation of the form y=mxy = mxy=mx, where mmm is the constant of proportionality.2. The line passes through the points (2,−15)(2, -15)(2,−15) and (6,−45)(6, -45)(6,−45).

STEP 2

To find the constant of proportionality mmm, we can use the two given points. The constant mmm is the ratio of the change in yyy to the change in xxx.m=ΔyΔxm = \frac{\Delta y}{\Delta x}m=ΔxΔy​

STEP 3

Calculate the change in yyy (Δy\Delta yΔy) using the yyy-coordinates of the given points.Δy=y2−y1\Delta y = y_2 - y_1Δy=y2​−y1​

STEP 4

Substitute the yyy-coordinates of the points into the formula.Δy=−45−(−15)\Delta y = -45 - (-15)Δy=−45−(−15)

STEP 5

Calculate the change in yyy.Δy=−45+15=−30\Delta y = -45 + 15 = -30Δy=−45+15=−30

STEP 6

Calculate the change in xxx (Δx\Delta xΔx) using the xxx-coordinates of the given points.Δx=x2−x1\Delta x = x_2 - x_1Δx=x2​−x1​

STEP 7

Substitute the xxx-coordinates of the points into the formula.Δx=6−2\Delta x = 6 - 2Δx=6−2

STEP 8

Calculate the change in xxx.Δx=6−2=4\Delta x = 6 - 2 = 4Δx=6−2=4

STEP 9

Now, calculate the constant of proportionality mmm using the changes in yyy and xxx.m=ΔyΔxm = \frac{\Delta y}{\Delta x}m=ΔxΔy​

STEP 10

Substitute the values for Δy\Delta yΔy and Δx\Delta xΔx into the formula.m=−304m = \frac{-30}{4}m=4−30​

STEP 11

Calculate the constant of proportionality mmm.m=−304=−7.5m = \frac{-30}{4} = -7.5m=4−30​=−7.5

STEP 12

Now that we have the constant of proportionality mmm, we can write the equation of the proportional relationship.y=mxy = mxy=mx

STEP 13

Substitute the value of mmm into the equation.y=−7.5xy = -7.5xy=−7.5xThe equation for the proportional relationship that passes through the points (2,−15)(2,-15)(2,−15) and (6,−45)(6,-45)(6,−45) is y=−7.5xy = -7.5xy=−7.5x.

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

Find the equation $y=mx$ for the proportional relationship passing through the points $(2,-15)$ and $(6,-45)$ .

Assumptions
1. The relationship between $x$ and $y$ is proportional, which means it can be described by an equation of the form $y = mx$ , where $m$ is the constant of proportionality.
2. The line passes through the points $(2, -15)$ and $(6, -45)$ .

To find the constant of proportionality $m$ , we can use the two given points. The constant $m$ is the ratio of the change in $y$ to the change in $x$ .
$m = \frac{\Delta y}{\Delta x}$

Calculate the change in $y$ ( $\Delta y$ ) using the $y$ -coordinates of the given points.
$\Delta y = y_2 - y_1$

Substitute the $y$ -coordinates of the points into the formula.
$\Delta y = -45 - (-15)$

Calculate the change in $y$ .
$\Delta y = -45 + 15 = -30$

Calculate the change in $x$ ( $\Delta x$ ) using the $x$ -coordinates of the given points.
$\Delta x = x_2 - x_1$

Substitute the $x$ -coordinates of the points into the formula.
$\Delta x = 6 - 2$

Calculate the change in $x$ .
$\Delta x = 6 - 2 = 4$

Now, calculate the constant of proportionality $m$ using the changes in $y$ and $x$ .
$m = \frac{\Delta y}{\Delta x}$

Substitute the values for $\Delta y$ and $\Delta x$ into the formula.
$m = \frac{-30}{4}$

Calculate the constant of proportionality $m$ .
$m = \frac{-30}{4} = -7.5$

Now that we have the constant of proportionality $m$ , we can write the equation of the proportional relationship.
$y = mx$

Substitute the value of $m$ into the equation.
$y = -7.5x$
The equation for the proportional relationship that passes through the points $(2,-15)$ and $(6,-45)$ is $y = -7.5x$ .