(0,4) , 3x+8y=4

Question

Write the slope-intercept form of an equation that passes through the given point and is perpendicular to the graph of each equation.

Answer 1

Hi Gabby;

(0,4) , 3x+8y=4

The equation is in standard form...

Ax+By=C...A>0

Slope is -A/B

Slope is -3/8

The slope of the equation perpendicular to this is such negative inverse...

Slope is 8/3

Slope-intercept equation is...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.  This is provided, (0,4)...

y=(8/3)x+4

Answer 2

I want to answer this with as few words as possible so here is my short answer (just ask if you want the longer one):

 

Our line is to be in slope-intercept form. Slope-intercept form is y= mx + b. 

Since (0,4) is a point, the y-intercept ("b") is 4.

 

The perpendicular line, 3x + 8y = 4, is in standard form: Ax + By = C where A = 3, B = 8 and C = 4.

 

Since our line is perpendicular to 3x + 8y = 4 the slope of our line is the negative reciprocal of "-A/B or -3/8". The negative reciprocal would therefore be 8/3 (flip the fraction's numerator and denominator and take the negative of a negative - which is a positive).

 

Therefore you substitute 8/3 for "m" and 4 for "b" in the equation y = mx + b you get ....

 

I'll let the reader fill in the blank.