Write the equation of the line in standard form if it has a slope of -1/4 and has an x-intercept of 8.

Answer 1

Write the equation of the line in standard form if it has a slope of -1/4 and has an x-intercept of 8.

Most courses, teachers, and tutors will tell you to:

(1) use the slope-intercept form or an equation of a line since the slope is given (-1/4).

Then, (2) either use the point-slope form using the point (8,0) or just plug in x=8 and y=0 to find b (the y-intercept).

HOWEVER, by Algebra 2, you have converted formulas so many times that you should have noticed:

Standard Form: Ax+By=C

Slope: -A/B

x-intercept (place where y=0): C/A

So,

the equation (in Standard Form) is:

x + 4y = 8

Answer 2

slope = m = -1/4

x-intercept = ( 8, 0 )

applying this information to the slope-intercept equation of the line y = mx + b

we get 0 = (-1/4)(8) + b = - 2 + b

and solving for b, we get b = 2

substituting all this information on the equation y = mx + b

we get y = ( -1/4 )x + 2

multiplying on both sides by - 4, we get - 4y = x + 2

which we need to write in standard form ax + by = c

our equation then becomes x + 4y = - 2