Solved on Jan 17, 2024

Find the equation of a line with y-intercept $9$ and x-intercept $-4$ .

STEP 1

Assumptions
1. The line has a specific y-axis value (y-intercept) of 9.
2. The line has a specific x-axis value (x-intercept) of -4.
3. We are looking for the equation of a straight line in the slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To find the equation of the line, we need to determine its slope. The slope $m$ of a line can be found using the coordinates of two points on the line. In this case, we have the x-intercept and y-intercept, which give us two points: $(x_1, y_1) = (-4, 0)$ and $(x_2, y_2) = (0, 9)$ .

STEP 3

Calculate the slope $m$ using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 4

Substitute the coordinates of the two points into the slope formula:
$m = \frac{9 - 0}{0 - (-4)}$

STEP 5

Simplify the expression to find the slope:
$m = \frac{9}{4}$

STEP 6

Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:
$y = mx + b$

STEP 7

Substitute the slope $m = \frac{9}{4}$ and the y-intercept $b = 9$ into the equation:
$y = \frac{9}{4}x + 9$
This is the equation of the line.

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Find the equation of a line with y-intercept $9$ and x-intercept $-4$ .

STEP 1

Assumptions
1. The line has a specific y-axis value (y-intercept) of 9.
2. The line has a specific x-axis value (x-intercept) of -4.
3. We are looking for the equation of a straight line in the slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To find the equation of the line, we need to determine its slope. The slope $m$ of a line can be found using the coordinates of two points on the line. In this case, we have the x-intercept and y-intercept, which give us two points: $(x_1, y_1) = (-4, 0)$ and $(x_2, y_2) = (0, 9)$ .

STEP 3

Calculate the slope $m$ using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 4

Substitute the coordinates of the two points into the slope formula:
$m = \frac{9 - 0}{0 - (-4)}$

STEP 5

Simplify the expression to find the slope:
$m = \frac{9}{4}$

STEP 6

Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:
$y = mx + b$

STEP 7

Substitute the slope $m = \frac{9}{4}$ and the y-intercept $b = 9$ into the equation:
$y = \frac{9}{4}x + 9$
This is the equation of the line.

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Find the equation of a line with y-intercept 999 and x-intercept −4-4−4.

STEP 1

Assumptions1. The line has a specific y-axis value (y-intercept) of 9.2. The line has a specific x-axis value (x-intercept) of -4.3. We are looking for the equation of a straight line in the slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

STEP 3

Calculate the slope mmm using the formula:m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​

STEP 4

Substitute the coordinates of the two points into the slope formula:m=9−00−(−4)m = \frac{9 - 0}{0 - (-4)}m=0−(−4)9−0​

STEP 5

Simplify the expression to find the slope:m=94m = \frac{9}{4}m=49​

STEP 6

Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:y=mx+by = mx + by=mx+b

STEP 7

Substitute the slope m=94m = \frac{9}{4}m=49​ and the y-intercept b=9b = 9b=9 into the equation:y=94x+9y = \frac{9}{4}x + 9y=49​x+9This is the equation of the line.

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Find the equation of a line with y-intercept $9$ and x-intercept $-4$ .

Assumptions
1. The line has a specific y-axis value (y-intercept) of 9.
2. The line has a specific x-axis value (x-intercept) of -4.
3. We are looking for the equation of a straight line in the slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Calculate the slope $m$ using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates of the two points into the slope formula:
$m = \frac{9 - 0}{0 - (-4)}$

Simplify the expression to find the slope:
$m = \frac{9}{4}$

Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:
$y = mx + b$

Substitute the slope $m = \frac{9}{4}$ and the y-intercept $b = 9$ into the equation:
$y = \frac{9}{4}x + 9$
This is the equation of the line.