Question Find the linear equation $y = mx + b$ that represents the relationship between $x$ and $y$ given the table: $(-4, 1), (-2, 1.5), (4, 3), (6, 3.5)$ .

Studdy Solution

STEP 1

Assumptions1. The relationship between $x$ and $y$ is linear, which can be represented by the equation $y = mx + b$ . . The values of $x$ and $y$ in the table are accurate and consistent.

STEP 2

First, we need to find the slope ( $m$ ) of the line. The slope can be calculated using the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

We can use any two points from the table to calculate the slope. Let's use the points (-,1) and (,3). Plug these values into the slope formula.
$m = \frac{3 -1}{ - (-)}$

STEP 4

implify the equation to calculate the slope.
$m = \frac{2}{8} =0.25$

STEP 5

Now that we have the slope, we can find the y-intercept ( $b$ ). We can do this by rearranging the equation $y = mx + b$ to solve for $b$ $b = y - mx$

STEP 6

We can use any point from the table to calculate the y-intercept. Let's use the point (-4,1). Plug these values into the equation for $b$ .
$b =1 -0.25 \times (-4)$

STEP 7

implify the equation to calculate the y-intercept.
$b =1 +1 =2$

STEP 8

Now that we have both the slope and the y-intercept, we can write the equation of the line. Plug the values of $m$ and $b$ into the equation $y = mx + b$ .
$y =0.25x +2$ The equation that represents the relationship between $x$ and $y$ is $y =0.25x +2$ .

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Question Find the linear equation $y = mx + b$ that represents the relationship between $x$ and $y$ given the table: $(-4, 1), (-2, 1.5), (4, 3), (6, 3.5)$ .

Studdy Solution

STEP 1

Assumptions1. The relationship between $x$ and $y$ is linear, which can be represented by the equation $y = mx + b$ . . The values of $x$ and $y$ in the table are accurate and consistent.

STEP 2

First, we need to find the slope ( $m$ ) of the line. The slope can be calculated using the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

We can use any two points from the table to calculate the slope. Let's use the points (-,1) and (,3). Plug these values into the slope formula.
$m = \frac{3 -1}{ - (-)}$

STEP 4

implify the equation to calculate the slope.
$m = \frac{2}{8} =0.25$

STEP 5

Now that we have the slope, we can find the y-intercept ( $b$ ). We can do this by rearranging the equation $y = mx + b$ to solve for $b$ $b = y - mx$

STEP 6

We can use any point from the table to calculate the y-intercept. Let's use the point (-4,1). Plug these values into the equation for $b$ .
$b =1 -0.25 \times (-4)$

STEP 7

implify the equation to calculate the y-intercept.
$b =1 +1 =2$

STEP 8

Now that we have both the slope and the y-intercept, we can write the equation of the line. Plug the values of $m$ and $b$ into the equation $y = mx + b$ .
$y =0.25x +2$ The equation that represents the relationship between $x$ and $y$ is $y =0.25x +2$ .

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Question Find the linear equation y=mx+by = mx + by=mx+b that represents the relationship between xxx and yyy given the table: (−4,1),(−2,1.5),(4,3),(6,3.5)(-4, 1), (-2, 1.5), (4, 3), (6, 3.5)(−4,1),(−2,1.5),(4,3),(6,3.5).

Studdy Solution

STEP 1

Assumptions1. The relationship between xxx and yyy is linear, which can be represented by the equation y=mx+by = mx + by=mx+b. . The values of xxx and yyy in the table are accurate and consistent.

STEP 2

First, we need to find the slope (mmm) of the line. The slope can be calculated using the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

We can use any two points from the table to calculate the slope. Let's use the points (-,1) and (,3). Plug these values into the slope formula.m=3−1−(−)m = \frac{3 -1}{ - (-)}m=−(−)3−1​

STEP 4

implify the equation to calculate the slope.m=28=0.25m = \frac{2}{8} =0.25m=82​=0.25

STEP 5

Now that we have the slope, we can find the y-intercept (bbb). We can do this by rearranging the equation y=mx+by = mx + by=mx+b to solve for bbbb=y−mxb = y - mxb=y−mx

STEP 6

We can use any point from the table to calculate the y-intercept. Let's use the point (-4,1). Plug these values into the equation for bbb.b=1−0.25×(−4)b =1 -0.25 \times (-4)b=1−0.25×(−4)

STEP 7

implify the equation to calculate the y-intercept.b=1+1=2b =1 +1 =2b=1+1=2

STEP 8

Now that we have both the slope and the y-intercept, we can write the equation of the line. Plug the values of mmm and bbb into the equation y=mx+by = mx + by=mx+b.y=0.25x+2y =0.25x +2y=0.25x+2The equation that represents the relationship between xxx and yyy is y=0.25x+2y =0.25x +2y=0.25x+2.

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Question Find the linear equation $y = mx + b$ that represents the relationship between $x$ and $y$ given the table: $(-4, 1), (-2, 1.5), (4, 3), (6, 3.5)$ .

Assumptions1. The relationship between $x$ and $y$ is linear, which can be represented by the equation $y = mx + b$ . . The values of $x$ and $y$ in the table are accurate and consistent.

First, we need to find the slope ( $m$ ) of the line. The slope can be calculated using the formula $m = \frac{y2 - y1}{x2 - x1}$

We can use any two points from the table to calculate the slope. Let's use the points (-,1) and (,3). Plug these values into the slope formula.
$m = \frac{3 -1}{ - (-)}$

implify the equation to calculate the slope.
$m = \frac{2}{8} =0.25$

Now that we have the slope, we can find the y-intercept ( $b$ ). We can do this by rearranging the equation $y = mx + b$ to solve for $b$ $b = y - mx$

We can use any point from the table to calculate the y-intercept. Let's use the point (-4,1). Plug these values into the equation for $b$ .
$b =1 -0.25 \times (-4)$

implify the equation to calculate the y-intercept.
$b =1 +1 =2$

Now that we have both the slope and the y-intercept, we can write the equation of the line. Plug the values of $m$ and $b$ into the equation $y = mx + b$ .
$y =0.25x +2$ The equation that represents the relationship between $x$ and $y$ is $y =0.25x +2$ .