QuestionFind the slope-intercept form of the line with $x$ -intercept $(-6,0)$ and $y$ -intercept $(0,5)$ .

Studdy Solution

STEP 1

Assumptions1. The x-intercept is (-6,0) . The y-intercept is (0,5)
3. The line is linear and in two dimensions4. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept

STEP 2

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ .
$m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for the x-intercept and y-intercept to calculate the slope.
$m = \frac{0 -5}{-6 -0}$

STEP 4

Calculate the slope.
$m = \frac{-}{-6} = \frac{}{6}$

STEP 5

Now that we have the slope, we can write the equation of the line in slope-intercept form. The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which is given as5.
$y = mx + b$

STEP 6

Plug in the values for the slope and the y-intercept to write the equation of the line.
$y = \frac{5}{6}x +5$ The equation of the line in slope-intercept form is $y = \frac{5}{6}x +5$ .

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QuestionFind the slope-intercept form of the line with $x$ -intercept $(-6,0)$ and $y$ -intercept $(0,5)$ .

Studdy Solution

STEP 1

Assumptions1. The x-intercept is (-6,0) . The y-intercept is (0,5)
3. The line is linear and in two dimensions4. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept

STEP 2

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ .
$m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for the x-intercept and y-intercept to calculate the slope.
$m = \frac{0 -5}{-6 -0}$

STEP 4

Calculate the slope.
$m = \frac{-}{-6} = \frac{}{6}$

STEP 5

Now that we have the slope, we can write the equation of the line in slope-intercept form. The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which is given as5.
$y = mx + b$

STEP 6

Plug in the values for the slope and the y-intercept to write the equation of the line.
$y = \frac{5}{6}x +5$ The equation of the line in slope-intercept form is $y = \frac{5}{6}x +5$ .

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QuestionFind the slope-intercept form of the line with xxx-intercept (−6,0)(-6,0)(−6,0) and yyy-intercept (0,5)(0,5)(0,5).

Studdy Solution

STEP 1

Assumptions1. The x-intercept is (-6,0) . The y-intercept is (0,5)3. The line is linear and in two dimensions4. The slope-intercept form of a line is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept

STEP 2

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

STEP 3

Now, plug in the given values for the x-intercept and y-intercept to calculate the slope.m=0−5−6−0m = \frac{0 -5}{-6 -0}m=−6−00−5​

STEP 4

Calculate the slope.m=−−6=6m = \frac{-}{-6} = \frac{}{6}m=−6−​=6​

STEP 5

Now that we have the slope, we can write the equation of the line in slope-intercept form. The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which is given as5.y=mx+by = mx + by=mx+b

STEP 6

Plug in the values for the slope and the y-intercept to write the equation of the line.y=56x+5y = \frac{5}{6}x +5y=65​x+5The equation of the line in slope-intercept form is y=56x+5y = \frac{5}{6}x +5y=65​x+5.

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QuestionFind the slope-intercept form of the line with $x$ -intercept $(-6,0)$ and $y$ -intercept $(0,5)$ .

Assumptions1. The x-intercept is (-6,0) . The y-intercept is (0,5)
3. The line is linear and in two dimensions4. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ .
$m = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for the x-intercept and y-intercept to calculate the slope.
$m = \frac{0 -5}{-6 -0}$

Calculate the slope.
$m = \frac{-}{-6} = \frac{}{6}$

Now that we have the slope, we can write the equation of the line in slope-intercept form. The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which is given as5.
$y = mx + b$

Plug in the values for the slope and the y-intercept to write the equation of the line.
$y = \frac{5}{6}x +5$ The equation of the line in slope-intercept form is $y = \frac{5}{6}x +5$ .