Indicate the equation of the line through (2, -4) and having slope of 3/5.

To find the equation of a line, you need its slope and a point it passes through. In this case, you are given the slope of the line (3/5) and a point through which the line passes (2, -4).

The equation of a line is typically represented in slope-intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept.

Step 1: Use the point-slope form of a line
The point-slope form of a line is: y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point and "m" is the slope.
Using the given point (2, -4) and slope (3/5), we have:

y - (-4) = (3/5)(x - 2)

Simplifying further:

y + 4 = (3/5)(x - 2)

Step 2: Convert to slope-intercept form
To convert the equation to slope-intercept form, we need to rearrange it to solve for y:

y + 4 = (3/5)(x - 2)

Distribute (3/5) to both terms inside the parentheses:

y + 4 = (3/5)x - (3/5)(2)
y + 4 = (3/5)x - 6/5

Now, move the constant term (4) to the right side of the equation:

y = (3/5)x - 6/5 - 4

Simplify and combine the terms on the right side:

y = (3/5)x - 6/5 - 20/5
y = (3/5)x - 26/5

So, the equation of the line passing through (2, -4) with a slope of 3/5 is y = (3/5)x - 26/5.

Line L passes through (x0,y0) with slope m has the equation:

L : (y-y0)=m(x-x0)
Substitute the given values into the equation and simplify.