Question

Use the information given to write an equation in standard form.

6. Slope is 3, and (1, 4) is on the line, 7. Slope is -2, and (4, 3) is on the line.
8.
Slope is –3, and (0, -4) is on the line. 9.
Slope is 0, and (0,5) is on the line.

Answer 1

6. 3x -y = -1

7. 2x +y = 11

8. 3x +y = -4

9. y = 5

Explanation:

When a point and a slope are given, it is often useful to start by writing the equation of the line in point-slope form:

y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Rewrite of point-slope equation

The standard form equation of a line has the form ...

ax +by = c

where a, b, c are mutually prime integers, and a > 0.

Rewriting the point-slope equation to this form, we have ...

y -k = mx -mh . . . . . eliminate parentheses

mx -y = mh -k . . . . . . add mh-y to both sides (Works for m > 0)

If the slope is negative, then we need to multiply by -1:

-mx +y = k -mh

Using these equations in the given problems, we have ...

6. m=3, (h, k) = (1, 4)

The slope is greater than 0, so our equation is ...

mx -y = mh -k

3x -y = 3(1) -4

3x -y = -1

7. m=-2, (h, k) = (4, 3)

The slope is less than 0, so our equation is ...

-mx +y = k -mh

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

2x +y = 11

8. m=-3, (h, k) = (0, -4)

As in problem 7,

-mx +y = k -mh

-(-3)x +y = (-4) -(-3)(0)

3x +y = -4

9. m=0, (h, k) = (0, 5)

We require the coefficient of y to be positive, so we need to use the second form.

-mx +y = k -mh

-(0)x +y = 5 -(0)(0)

y = 5