Question

What is the equation of a line (in standard form) that passes through point A(1,-4) and has a slope of 3/4?

Answer 1

Answer:

3x-4y=19

Step-by-step explanation:

Hi there!

We want to write the equation of the line in standard form that passes through the point (1, -4) and has the slope of 3/4

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative

First, in order to find ax+by=c, we'll need to get slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we already know the slope (3/4), we can substitute it into the formula for y=mx+b.

y=3/4x+b

Now we need to solve for b

Since the equation passes through the point (1, -4), we can use it to solve for b

Substitute 1 as x and -4 as y.

-4=3/4(1)+b

Multiply

-4=3/4+b

Subtract 3/4 from both sides

-19/4=b

Now substitute -19/4 as b into the equation

y=3/4x-19/4

Now we have the equation in slope-intercept form, but remember, we want it in standard form

Since x and y are on the same side in standard form, subtract 3/4x from both sides

-3/4x+y=-19/4

Remember that a cannot be negative, and the coefficients are integers (they cannot be fractions)

So in order to clear the fractions and change the sign of the equation, multiply both sides by -4

-4(-3/4x+y)=-4(-19/4)

Multiply

3x-4y=19

Hope this helps!