Question Write the linear function $f(x)$ that passes through the points $(-4, -7)$ and $(1, 4)$ , then sketch the graph.

Studdy Solution

STEP 1

Assumptions1. The function $f$ is linear, meaning it can be written in the form $f(x) = mx + b$ where $m$ is the slope and $b$ is the y-intercept. . We are given two points on the line $(-4, -7)$ and $(1,4)$ .

STEP 2

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

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{ - (-7)}{1 - (-)}$

STEP 4

implify the numerator and the denominator.
$m = \frac{4 +7}{1 +4}$

STEP 5

Calculate the slope.
$m = \frac{11}{5} =2.2$

STEP 6

Now that we have the slope, we can find the y-intercept $b$ by rearranging the equation of the line and plugging in the values for one of the given points and the slope. Let's use the point $(1,4)$ .
$b = y - mx$

STEP 7

Plug in the values for $x$ , $y$ , and $m$ to calculate the y-intercept.
$b =4 -2.2 \times1$

STEP 8

Calculate the y-intercept.
$b =4 -2.2 =1.8$

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the line.
$f(x) =2.2x +.8$

STEP 10

To sketch the graph of the function, start by plotting the y-intercept $(0,.8)$ on the y-axis.

STEP 11

Then, from the y-intercept, use the slope to find another point on the line. The slope is $.$ , which means for every unit we move to the right along the x-axis, we move up by $.$ units along the y-axis.

STEP 12

Draw a straight line through the two points to complete the graph.
The linear function is $f(x) =2.2x +.8$ and its graph is a straight line through the points $(0,.8)$ and $(,4)$ .

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Question Write the linear function $f(x)$ that passes through the points $(-4, -7)$ and $(1, 4)$ , then sketch the graph.

Studdy Solution

STEP 1

Assumptions1. The function $f$ is linear, meaning it can be written in the form $f(x) = mx + b$ where $m$ is the slope and $b$ is the y-intercept. . We are given two points on the line $(-4, -7)$ and $(1,4)$ .

STEP 2

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

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{ - (-7)}{1 - (-)}$

STEP 4

implify the numerator and the denominator.
$m = \frac{4 +7}{1 +4}$

STEP 5

Calculate the slope.
$m = \frac{11}{5} =2.2$

STEP 6

Now that we have the slope, we can find the y-intercept $b$ by rearranging the equation of the line and plugging in the values for one of the given points and the slope. Let's use the point $(1,4)$ .
$b = y - mx$

STEP 7

Plug in the values for $x$ , $y$ , and $m$ to calculate the y-intercept.
$b =4 -2.2 \times1$

STEP 8

Calculate the y-intercept.
$b =4 -2.2 =1.8$

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the line.
$f(x) =2.2x +.8$

STEP 10

To sketch the graph of the function, start by plotting the y-intercept $(0,.8)$ on the y-axis.

STEP 11

Then, from the y-intercept, use the slope to find another point on the line. The slope is $.$ , which means for every unit we move to the right along the x-axis, we move up by $.$ units along the y-axis.

STEP 12

Draw a straight line through the two points to complete the graph.
The linear function is $f(x) =2.2x +.8$ and its graph is a straight line through the points $(0,.8)$ and $(,4)$ .

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Question Write the linear function f(x)f(x)f(x) that passes through the points (−4,−7)(-4, -7)(−4,−7) and (1,4)(1, 4)(1,4), then sketch the graph.

Studdy Solution

STEP 1

Assumptions1. The function fff is linear, meaning it can be written in the form f(x)=mx+bf(x) = mx + bf(x)=mx+b where mmm is the slope and bbb is the y-intercept. . We are given two points on the line (−4,−7)(-4, -7)(−4,−7) and (1,4)(1,4)(1,4).

STEP 2

First, we need to find the slope of the line. The slope mmm 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 x1x1x1, y1y1y1, x2x2x2, and y2y2y2 to calculate the slope.m=−(−7)1−(−)m = \frac{ - (-7)}{1 - (-)}m=1−(−)−(−7)​

STEP 4

implify the numerator and the denominator.m=4+71+4m = \frac{4 +7}{1 +4}m=1+44+7​

STEP 5

Calculate the slope.m=115=2.2m = \frac{11}{5} =2.2m=511​=2.2

STEP 6

Now that we have the slope, we can find the y-intercept bbb by rearranging the equation of the line and plugging in the values for one of the given points and the slope. Let's use the point (1,4)(1,4)(1,4).b=y−mxb = y - mxb=y−mx

STEP 7

Plug in the values for xxx, yyy, and mmm to calculate the y-intercept.b=4−2.2×1b =4 -2.2 \times1b=4−2.2×1

STEP 8

Calculate the y-intercept.b=4−2.2=1.8b =4 -2.2 =1.8b=4−2.2=1.8

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the line.f(x)=2.2x+.8f(x) =2.2x +.8f(x)=2.2x+.8

STEP 10

To sketch the graph of the function, start by plotting the y-intercept (0,.8)(0,.8)(0,.8) on the y-axis.

STEP 11

Then, from the y-intercept, use the slope to find another point on the line. The slope is ..., which means for every unit we move to the right along the x-axis, we move up by ... units along the y-axis.

STEP 12

Draw a straight line through the two points to complete the graph.The linear function is f(x)=2.2x+.8f(x) =2.2x +.8f(x)=2.2x+.8 and its graph is a straight line through the points (0,.8)(0,.8)(0,.8) and (,4)(,4)(,4).

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

Question Write the linear function $f(x)$ that passes through the points $(-4, -7)$ and $(1, 4)$ , then sketch the graph.

Assumptions1. The function $f$ is linear, meaning it can be written in the form $f(x) = mx + b$ where $m$ is the slope and $b$ is the y-intercept. . We are given two points on the line $(-4, -7)$ and $(1,4)$ .

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

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{ - (-7)}{1 - (-)}$

implify the numerator and the denominator.
$m = \frac{4 +7}{1 +4}$

Calculate the slope.
$m = \frac{11}{5} =2.2$

Now that we have the slope, we can find the y-intercept $b$ by rearranging the equation of the line and plugging in the values for one of the given points and the slope. Let's use the point $(1,4)$ .
$b = y - mx$

Plug in the values for $x$ , $y$ , and $m$ to calculate the y-intercept.
$b =4 -2.2 \times1$

Calculate the y-intercept.
$b =4 -2.2 =1.8$

Now that we have the slope and the y-intercept, we can write the equation of the line.
$f(x) =2.2x +.8$

To sketch the graph of the function, start by plotting the y-intercept $(0,.8)$ on the y-axis.

Then, from the y-intercept, use the slope to find another point on the line. The slope is $.$ , which means for every unit we move to the right along the x-axis, we move up by $.$ units along the y-axis.

Draw a straight line through the two points to complete the graph.
The linear function is $f(x) =2.2x +.8$ and its graph is a straight line through the points $(0,.8)$ and $(,4)$ .