Question

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Passing through (- 9. - 4) and parallel to the line whose equation is y = - 4x + 3
Write an equation for the line in point-slope form.

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 3 ← is in slope- intercept form

with slope m = - 4

• Parallel lines have equal slopes, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 9, - 4) into the partial equation

- 4 = 36 + c ⇒ c = - 4 - 36 = - 40

y = - 4x - 40 ← in slope- intercept form

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 4 and (a, b) = (- 9, - 4), thus

y - (- 4) = - 4(x - (- 9)), that is

y + 4 = - 4(x + 9) ← in point- slope form