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.