Question

Write 4x – 2y + 3 = 1 in slope-intercept form. All variables must

be lower case and do not leave any spaces in your response.

Answer 1

y = 2x + 1.

Explanation:

The slope-intercept equation of a line is in the form:

y = mx + b,

where

• m is the slope of the line, and
• (0, b) is the y-intercept of the line.

The coefficient in front of y is now 2. Reduce this coefficient to 1. Multiply both sides of the equation by 1/2:

2x - y + 3/2 = 1/2.

Separate y from x and the constant. Add y - 1/2 to both sides of this equation:

y = 2x + 1.

This expression satisfies the form y = mx + b:

• m = 2,
• b = 1.

Answer 2

`\bf 4x-2y+3=1\implies 4x-2y = -2\implies -2y=-4x-2\implies y=\cfrac{-4x-2}{-2} \\\\\\ y=\cfrac{-4x}{-2}+\cfrac{-2}{-2}\implies y=2x+1\qquad \impliedby \begin{array}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}`