the equation $y - \frac{7}{2} = \frac{1}{2}(x - 4)$ is written in point-slope form. what is the $y$-intercept of the equation?

$-\frac{11}{2}$

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

Question

the equation $y - \frac{7}{2} = \frac{1}{2}(x - 4)$ is written in point-slope form. what is the $y$-intercept of the equation?

$-\frac{11}{2}$

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Point-Slope Form", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Point-Slope Form", "Slope-Intercept Form", "Linear Equation Interpretation" ] } ## Identify the given equation Using the *Point-Slope Form* knowledge point $$ y - \frac{7}{2} = \frac{1}{2}(x - 4) $$ ## Distribute the slope on the right side Using the *Slope-Intercept Form* knowledge point $$ y - \frac{7}{2} = \frac{1}{2}x - 2 $$ ## Isolate y to find the y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} y &= \frac{1}{2}x - 2 + \frac{7}{2} \ y &= \frac{1}{2}x - \frac{4}{2} + \frac{7}{2} \ y &= \frac{1}{2}x + \frac{3}{2} \end{aligned} $$ The $y$-intercept is $\frac{3}{2}$.

(A) $-\frac{11}{2}$

(B) $-\frac{1}{2}$

(C) $\frac{1}{2}$

(D) $\frac{3}{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given equation

Distribute the slope on the right side

Isolate y to find the y-intercept

Answer: