Question

Consider the line 6x + 8y = 7. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answer 1

So, the slope of a line parallel is 4/3.​

Explanation:

The equation of the line is given as 6x+8y=7

. We can rewrite this in the slope-intercept form y=mx+b

, where m

is the slope of the line.

Rearranging the given equation, we get y=−4/3​x+8/7​

. So, the slope of the given line is −4/3​

.

The slope of a line parallel to this line would be the same as the slope of this line, which is −4/3​

.

The slope of a line perpendicular to this line would be the negative reciprocal of the slope of this line. So, it would be −​1 3/4=3/4​

.

So, the slope of a line parallel to the given line is −4/3​ and the slope of a line perpendicular to the given line is 4/3.​

Answer 2

y = mx + b

6x + 8y = 7

8y = 7 - 6x

y = -⁶/₈X + ⁷/₈

so the parallel slope = -⁶/₈ = -³/₄

and the perpendicular is = ⁴/₃