QuestionConvert $2x + 5y = 12$ to slope-intercept form, $y = mx + b$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is a linear equation in the form $ax + by = c$ . . We need to find the slope-intercept form of the line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To find the slope-intercept form, we need to isolate $y$ in the given equation. We can do this by subtracting $2x$ from both sides of the equation.
$5y =12 -2x$

STEP 3

Next, we divide both sides of the equation by $5$ to solve for $y$ .
$y = \frac{12 -2x}{5}$

STEP 4

We can rewrite the right side of the equation to match the slope-intercept form $y = mx + b$ . This involves rearranging the terms so that the $x$ term comes first.
$y = \frac{-2x +12}{}$

STEP 5

We can further simplify this by dividing each term in the numerator by $5$ .
$y = -\frac{2}{5}x + \frac{12}{5}$ So, the slope-intercept form of the given line is $y = -\frac{2}{5}x + \frac{12}{5}$ .

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QuestionConvert $2x + 5y = 12$ to slope-intercept form, $y = mx + b$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is a linear equation in the form $ax + by = c$ . . We need to find the slope-intercept form of the line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To find the slope-intercept form, we need to isolate $y$ in the given equation. We can do this by subtracting $2x$ from both sides of the equation.
$5y =12 -2x$

STEP 3

Next, we divide both sides of the equation by $5$ to solve for $y$ .
$y = \frac{12 -2x}{5}$

STEP 4

We can rewrite the right side of the equation to match the slope-intercept form $y = mx + b$ . This involves rearranging the terms so that the $x$ term comes first.
$y = \frac{-2x +12}{}$

STEP 5

We can further simplify this by dividing each term in the numerator by $5$ .
$y = -\frac{2}{5}x + \frac{12}{5}$ So, the slope-intercept form of the given line is $y = -\frac{2}{5}x + \frac{12}{5}$ .

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QuestionConvert 2x+5y=122x + 5y = 122x+5y=12 to slope-intercept form, y=mx+by = mx + by=mx+b.

Studdy Solution

STEP 1

Assumptions1. The given equation is a linear equation in the form ax+by=cax + by = cax+by=c. . We need to find the slope-intercept form of the line, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

To find the slope-intercept form, we need to isolate yyy in the given equation. We can do this by subtracting 2x2x2x from both sides of the equation.5y=12−2x5y =12 -2x5y=12−2x

STEP 3

Next, we divide both sides of the equation by 555 to solve for yyy.y=12−2x5y = \frac{12 -2x}{5}y=512−2x​

STEP 4

We can rewrite the right side of the equation to match the slope-intercept form y=mx+by = mx + by=mx+b. This involves rearranging the terms so that the xxx term comes first.y=−2x+12y = \frac{-2x +12}{}y=−2x+12​

STEP 5

We can further simplify this by dividing each term in the numerator by 555.y=−25x+125y = -\frac{2}{5}x + \frac{12}{5}y=−52​x+512​So, the slope-intercept form of the given line is y=−25x+125y = -\frac{2}{5}x + \frac{12}{5}y=−52​x+512​.

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QuestionConvert $2x + 5y = 12$ to slope-intercept form, $y = mx + b$ .

Assumptions1. The given equation is a linear equation in the form $ax + by = c$ . . We need to find the slope-intercept form of the line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

To find the slope-intercept form, we need to isolate $y$ in the given equation. We can do this by subtracting $2x$ from both sides of the equation.
$5y =12 -2x$

Next, we divide both sides of the equation by $5$ to solve for $y$ .
$y = \frac{12 -2x}{5}$

We can rewrite the right side of the equation to match the slope-intercept form $y = mx + b$ . This involves rearranging the terms so that the $x$ term comes first.
$y = \frac{-2x +12}{}$

We can further simplify this by dividing each term in the numerator by $5$ .
$y = -\frac{2}{5}x + \frac{12}{5}$ So, the slope-intercept form of the given line is $y = -\frac{2}{5}x + \frac{12}{5}$ .