Math / Algebra

Question $2 x+5 y-10=0$ to slope/y-inter

Studdy Solution

STEP 1

1. The equation given is in the standard form of a linear equation: $Ax + By + C = 0$ .
2. We need to convert this equation to the slope-intercept form: $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Isolate the $y$ -term in the equation.
2. Solve for $y$ to express the equation in slope-intercept form.
3. Identify the slope and y-intercept from the equation.

STEP 3

Start with the given equation:
$2x + 5y - 10 = 0$
Our goal is to isolate the $y$ -term on one side of the equation.

STEP 4

To isolate the $y$ -term, move the $x$ -term and the constant term to the other side of the equation:
$5y = -2x + 10$

STEP 5

Solve for $y$ by dividing every term by the coefficient of $y$ , which is 5:
$y = -\frac{2}{5}x + 2$
Now the equation is in the slope-intercept form $y = mx + b$ .

STEP 6

Identify the slope and y-intercept from the equation $y = -\frac{2}{5}x + 2$ :
- The slope $m$ is $-\frac{2}{5}$ . - The y-intercept $b$ is $2$ .
The slope of the line is $-\frac{2}{5}$ and the y-intercept is $2$ .

Was this helpful?

Question $2 x+5 y-10=0$ to slope/y-inter

Studdy Solution

STEP 1

1. The equation given is in the standard form of a linear equation: $Ax + By + C = 0$ .
2. We need to convert this equation to the slope-intercept form: $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Isolate the $y$ -term in the equation.
2. Solve for $y$ to express the equation in slope-intercept form.
3. Identify the slope and y-intercept from the equation.

STEP 3

Start with the given equation:
$2x + 5y - 10 = 0$
Our goal is to isolate the $y$ -term on one side of the equation.

STEP 4

To isolate the $y$ -term, move the $x$ -term and the constant term to the other side of the equation:
$5y = -2x + 10$

STEP 5

Solve for $y$ by dividing every term by the coefficient of $y$ , which is 5:
$y = -\frac{2}{5}x + 2$
Now the equation is in the slope-intercept form $y = mx + b$ .

STEP 6

Identify the slope and y-intercept from the equation $y = -\frac{2}{5}x + 2$ :
- The slope $m$ is $-\frac{2}{5}$ . - The y-intercept $b$ is $2$ .
The slope of the line is $-\frac{2}{5}$ and the y-intercept is $2$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question2x+5y−10=02 x+5 y-10=02x+5y−10=0 to slope/y-inter

Studdy Solution

STEP 1

1. The equation given is in the standard form of a linear equation: Ax+By+C=0 Ax + By + C = 0 Ax+By+C=0.2. We need to convert this equation to the slope-intercept form: y=mx+b y = mx + b y=mx+b, where m m m is the slope and b b b is the y-intercept.

STEP 2

1. Isolate the y y y-term in the equation.2. Solve for y y y to express the equation in slope-intercept form.3. Identify the slope and y-intercept from the equation.

STEP 3

Start with the given equation:2x+5y−10=0 2x + 5y - 10 = 0 2x+5y−10=0Our goal is to isolate the y y y-term on one side of the equation.

STEP 4

To isolate the y y y-term, move the x x x-term and the constant term to the other side of the equation:5y=−2x+10 5y = -2x + 10 5y=−2x+10

STEP 5

Solve for y y y by dividing every term by the coefficient of y y y, which is 5:y=−25x+2 y = -\frac{2}{5}x + 2 y=−52​x+2Now the equation is in the slope-intercept form y=mx+b y = mx + b y=mx+b.

STEP 6

Identify the slope and y-intercept from the equation y=−25x+2 y = -\frac{2}{5}x + 2 y=−52​x+2:- The slope m m m is −25-\frac{2}{5}−52​. - The y-intercept b b b is 2 2 2. The slope of the line is −25-\frac{2}{5}−52​ and the y-intercept is 222.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $2 x+5 y-10=0$ to slope/y-inter

1. The equation given is in the standard form of a linear equation: $Ax + By + C = 0$ .
2. We need to convert this equation to the slope-intercept form: $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

1. Isolate the $y$ -term in the equation.
2. Solve for $y$ to express the equation in slope-intercept form.
3. Identify the slope and y-intercept from the equation.

Start with the given equation:
$2x + 5y - 10 = 0$
Our goal is to isolate the $y$ -term on one side of the equation.

To isolate the $y$ -term, move the $x$ -term and the constant term to the other side of the equation:
$5y = -2x + 10$

Solve for $y$ by dividing every term by the coefficient of $y$ , which is 5:
$y = -\frac{2}{5}x + 2$
Now the equation is in the slope-intercept form $y = mx + b$ .

Identify the slope and y-intercept from the equation $y = -\frac{2}{5}x + 2$ :
- The slope $m$ is $-\frac{2}{5}$ . - The y-intercept $b$ is $2$ .
The slope of the line is $-\frac{2}{5}$ and the y-intercept is $2$ .