Question

What is an equation of the line that passes through the point (2,3) and is parallel to

the line x + y = 4?

Answer 1

Explanation:

if the line equation is in the form

y = ...

the slope is always the factor of x.

x + y = 4

y = -x + 4

so, the slope is -1.

a parallel line has the same slope.

when having a surviving point we can use the point-slope form as equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

so,

y - 3 = -1(x - 2)

simplified we get

y - 3 = -x + 2

y = -x + 5

that would be the slope-intercept form (+5 being the interception point on the y-axis).