A line in the xy-plane is defined by the equation 5y - 2x = 15. What is the slope of the l… — SAT

A line in the $xy$ -plane is defined by the equation $5y - 2x = 15$ . What is the slope of the line?

The slope of the line is

\frac{2}{5}

To find the slope of the line, convert the equation

5y - 2x = 15

into slope-intercept form,

y = mx + b

, where

m

represents the slope. First, add

2x

to both sides to get

5y = 2x + 15

. Next, divide both sides by

5

to isolate

y

, yielding

y = \frac{2}{5}x + 3

. In this form, the coefficient of

x

is the slope, which is

\frac{2}{5}

Write the given equation of the line.

5y - 2x = 15

To identify the slope, we need to manipulate the given equation.

Isolate the

y

term on one side by adding

2x

to both sides.

5y = 2x + 15

This is the first step in converting the equation to slope-intercept form (

y = mx + b

Divide both sides of the equation by

5

to solve for

y

y = \frac{2}{5}x + 3

Dividing isolates

y

completely, putting the equation in the form

y = mx + b

, where

m

is the slope and

b

is the

y

-intercept.

Identify the slope

m

from the equation.

The slope

m

\frac{2}{5}

In the equation

y = \frac{2}{5}x + 3

, the coefficient of

x

represents the slope of the line.

Slope of a line from its equation

Question