Question

Find the y-intercept: y − 3 = 1/2x − 1

Answer 1

b = 2

Option A

Step-by-step explanation

Given that;

`\text{ y - 3 = }\frac{\text{ 1}}{\text{ 2}}x\text{ - 1}`

Follow the steps below to find the y-intercept

Recall, the slope-intercept equation is given as

y = mx + b

Where m is the slope of the line

b is the y-intercept

`\begin{gathered} \text{ y - 3 = }\frac{\text{ 1}}{\text{ 2}}x\text{ - 1} \\ \text{ } \\ \text{ y - 3 = }\frac{x\text{ - 2}}{\text{ 2}} \\ \text{ cross multiply} \\ \text{ 2\lparen y - 3\rparen = x - 2} \\ \text{ 2y - 6 = x - 2} \\ \text{ add 6 to both sides of the equation} \\ \text{ 2y - 6 + 6 = x - 2 + 6} \\ \text{ 2y = x + 4} \\ \text{ Divide both sides by 2} \\ \text{ }\frac{\text{ 2y}}{\text{ 2}}\text{ = }\frac{\text{ x}}{\text{ 2}}\text{ + }\frac{\text{ 4}}{\text{ 2}} \\ \text{ } \\ \text{ y = }\frac{\text{ 1}}{\text{ 2}}x\text{ + 2} \end{gathered}`

Recall, y = mx + b

b = 2

Therefore, the y-intercept (b) is 2