Question

What is the y-intercept and slope of 0=1-2y+14x? :)

Answer 1

$\bf 0=1-2y+14x\implies 2y=1+14x\implies 2y = 14x+1\implies y = \cfrac{14x+1}{2} \\\\\\ y = \cfrac{14x}{2}+\cfrac{1}{2}\implies y = \stackrel{\stackrel{m}{\downarrow }}{7} x+\cfrac{1}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

Answer 2

The y-intercept of the given equation is 0.5 and the slope is 7

From the question,

The given equation is 0=1-2y+14x

To determine the y-intercept and slope of the given equation,

We will express the given equation in the slope-intercept form of the equation of a straight line and then compare.

The slope-intercept form of the equation of a straight line is

y = mx + c

Where m is slope or gradient

and c is the y-intercept

Now, the given equation is

$0=1-2y+14x$

To express this in the slope-intercept form of the equation of a straight line,

First, add 2y to both sides

That is,

$0 +2y = 1-2y+2y+14x$

$2y = 1+14x$

$2y = 14x + 1$

Now, divide both sides by 2

$\frac{2y}{2} = \frac{14x +1}{2}$

∴ $y = 7x +\frac{1}{2}$

OR

$y = 7x +0.5$

Now, we will compare the equation to the slope-intercept form of the equation of a straight line y = mx + c

That is,

By comparing $y = 7x +0.5$ and y = mx +c

m = 7 and c = 0.5

∴ The y-intercept of the equation is 0.5

and the slope is 7

Hence, the y-intercept of the given equation is 0.5 and the slope is 7

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