Solved on Nov 08, 2023

Find the equation of a line given the slope $m=-4$ and a point $(1,8)$ on the line.

STEP 1

Assumptions1. We are given the slope of the line, m = -4. We are given a point on the line, (1,8)
3. We need to find the equation of the line in standard form. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

STEP 2

We start with the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

STEP 3

Substitute the given slope and point into the slope-intercept equation. The x and y values from the point replace x and y in the equation, and the given slope replaces m.
$8 = -(1) + b$

STEP 4

olve the equation for b to find the y-intercept.
$8 = -4 + b$

STEP 5

Add4 to both sides of the equation to isolate b.
$b =8 +4 =12$

STEP 6

Now that we have the y-intercept, we can write the equation of the line in slope-intercept form.
$y = -4x +12$

STEP 7

To convert the equation to standard form, we want to eliminate the fraction (if any) and make sure the coefficient of x is positive. Here, we don't have any fractions, but the coefficient of x is negative. So, we multiply the entire equation by -1.
$-y =4x -12$

STEP 8

Finally, we rearrange the equation to the standard form, Ax + By = C.
$4x + y =12$ So, the equation of the line in standard form is4x + y =12.

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Find the equation of a line given the slope $m=-4$ and a point $(1,8)$ on the line.

STEP 1

Assumptions1. We are given the slope of the line, m = -4. We are given a point on the line, (1,8)
3. We need to find the equation of the line in standard form. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

STEP 2

We start with the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

STEP 3

Substitute the given slope and point into the slope-intercept equation. The x and y values from the point replace x and y in the equation, and the given slope replaces m.
$8 = -(1) + b$

STEP 4

olve the equation for b to find the y-intercept.
$8 = -4 + b$

STEP 5

Add4 to both sides of the equation to isolate b.
$b =8 +4 =12$

STEP 6

Now that we have the y-intercept, we can write the equation of the line in slope-intercept form.
$y = -4x +12$

STEP 7

To convert the equation to standard form, we want to eliminate the fraction (if any) and make sure the coefficient of x is positive. Here, we don't have any fractions, but the coefficient of x is negative. So, we multiply the entire equation by -1.
$-y =4x -12$

STEP 8

Finally, we rearrange the equation to the standard form, Ax + By = C.
$4x + y =12$ So, the equation of the line in standard form is4x + y =12.

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Find the equation of a line given the slope m=−4m=-4m=−4 and a point (1,8)(1,8)(1,8) on the line.

STEP 1

Assumptions1. We are given the slope of the line, m = -4. We are given a point on the line, (1,8)3. We need to find the equation of the line in standard form. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

STEP 2

We start with the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

STEP 3

Substitute the given slope and point into the slope-intercept equation. The x and y values from the point replace x and y in the equation, and the given slope replaces m.8=−(1)+b8 = -(1) + b8=−(1)+b

STEP 4

olve the equation for b to find the y-intercept.8=−4+b8 = -4 + b8=−4+b

STEP 5

Add4 to both sides of the equation to isolate b.b=8+4=12b =8 +4 =12b=8+4=12

STEP 6

Now that we have the y-intercept, we can write the equation of the line in slope-intercept form.y=−4x+12y = -4x +12y=−4x+12

STEP 7

To convert the equation to standard form, we want to eliminate the fraction (if any) and make sure the coefficient of x is positive. Here, we don't have any fractions, but the coefficient of x is negative. So, we multiply the entire equation by -1.−y=4x−12-y =4x -12−y=4x−12

STEP 8

Finally, we rearrange the equation to the standard form, Ax + By = C.4x+y=124x + y =124x+y=12So, the equation of the line in standard form is4x + y =12.

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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 of a line given the slope $m=-4$ and a point $(1,8)$ on the line.

Assumptions1. We are given the slope of the line, m = -4. We are given a point on the line, (1,8)
3. We need to find the equation of the line in standard form. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

Substitute the given slope and point into the slope-intercept equation. The x and y values from the point replace x and y in the equation, and the given slope replaces m.
$8 = -(1) + b$

olve the equation for b to find the y-intercept.
$8 = -4 + b$

Add4 to both sides of the equation to isolate b.
$b =8 +4 =12$

Now that we have the y-intercept, we can write the equation of the line in slope-intercept form.
$y = -4x +12$

To convert the equation to standard form, we want to eliminate the fraction (if any) and make sure the coefficient of x is positive. Here, we don't have any fractions, but the coefficient of x is negative. So, we multiply the entire equation by -1.
$-y =4x -12$

Finally, we rearrange the equation to the standard form, Ax + By = C.
$4x + y =12$ So, the equation of the line in standard form is4x + y =12.