QuestionFind a linear equation for the line through $(1,4)$ with slope 6.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (1,4) . The slope of the line is63. The equation of a line is given by the formula $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

We can use the given point and the slope to find the y-intercept of the line. The formula to find the y-intercept is $c = y - mx$

STEP 3

Now, plug in the given values for $x$ , $y$ , and $m$ to calculate the y-intercept.
$c = -6(1)$

STEP 4

Calculate the y-intercept.
$c =4 -6 = -2$

STEP 5

Now that we have the slope and the y-intercept, we can write the equation of the line. The equation of a line is given by the formula $y = mx + c$ .

STEP 6

Plug in the values for $m$ and $c$ to write the equation of the line.
$y =6x -2$ So, the equation of the line that passes through the point (1,4) with a slope of6 is $y =6x -2$ .

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QuestionFind a linear equation for the line through $(1,4)$ with slope 6.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (1,4) . The slope of the line is63. The equation of a line is given by the formula $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

We can use the given point and the slope to find the y-intercept of the line. The formula to find the y-intercept is $c = y - mx$

STEP 3

Now, plug in the given values for $x$ , $y$ , and $m$ to calculate the y-intercept.
$c = -6(1)$

STEP 4

Calculate the y-intercept.
$c =4 -6 = -2$

STEP 5

Now that we have the slope and the y-intercept, we can write the equation of the line. The equation of a line is given by the formula $y = mx + c$ .

STEP 6

Plug in the values for $m$ and $c$ to write the equation of the line.
$y =6x -2$ So, the equation of the line that passes through the point (1,4) with a slope of6 is $y =6x -2$ .

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QuestionFind a linear equation for the line through (1,4)(1,4)(1,4) with slope 6.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (1,4) . The slope of the line is63. The equation of a line is given by the formula y=mx+cy = mx + cy=mx+c, where mmm is the slope and ccc is the y-intercept.

STEP 2

We can use the given point and the slope to find the y-intercept of the line. The formula to find the y-intercept isc=y−mxc = y - mxc=y−mx

STEP 3

Now, plug in the given values for xxx, yyy, and mmm to calculate the y-intercept.c=−6(1)c = -6(1)c=−6(1)

STEP 4

Calculate the y-intercept.c=4−6=−2c =4 -6 = -2c=4−6=−2

STEP 5

Now that we have the slope and the y-intercept, we can write the equation of the line. The equation of a line is given by the formula y=mx+cy = mx + cy=mx+c.

STEP 6

Plug in the values for mmm and ccc to write the equation of the line.y=6x−2y =6x -2y=6x−2So, the equation of the line that passes through the point (1,4) with a slope of6 is y=6x−2y =6x -2y=6x−2.

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QuestionFind a linear equation for the line through $(1,4)$ with slope 6.

Assumptions1. The line passes through the point (1,4) . The slope of the line is63. The equation of a line is given by the formula $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

We can use the given point and the slope to find the y-intercept of the line. The formula to find the y-intercept is $c = y - mx$

Now, plug in the given values for $x$ , $y$ , and $m$ to calculate the y-intercept.
$c = -6(1)$

Calculate the y-intercept.
$c =4 -6 = -2$

Now that we have the slope and the y-intercept, we can write the equation of the line. The equation of a line is given by the formula $y = mx + c$ .

Plug in the values for $m$ and $c$ to write the equation of the line.
$y =6x -2$ So, the equation of the line that passes through the point (1,4) with a slope of6 is $y =6x -2$ .