Question

find an equation of the line satisfying the given condition in standard form . Through {0, -35/3} ; slope 7/3

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis.

According to the statement data we have:

$m = \frac {7} {3}$

Thus, the equation is of the form:

$y = \frac {7} {3} x + b$

We substitute the given point and find the cut-off point:

$- \frac {35} {3} = \frac {7} {3} (0) + b\\- \frac {35} {3} = b$

Finally, the equation is:

$y = \frac {7} {3} x- \frac {35} {3}$

We manipulate algebraically to obtain the standard form:

We multiply by 3 on both sides of the equation:

$3y = 7x-35\\3y-7x = -35$

We multiply by -1 on both sides:

$7x-3y = 35$

Answer:

$7x-3y = 35$