what is the $y$-intercept of a line that has a slope of 3 and passes through point $(-1, -7)$?

$\bigcirc$ -10
$\bigcirc$ -4
$\bigcirc$ 3
$\bigcirc$ 7

Question

what is the $y$-intercept of a line that has a slope of 3 and passes through point $(-1, -7)$?

$\bigcirc$ -10
$\bigcirc$ -4
$\bigcirc$ 3
$\bigcirc$ 7

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Point-Slope Form", "Linear Equation Graphing" ] } ## Identify the given values Using the *Slope-Intercept Form* and *Point-Slope Form* knowledge points $$ \begin{aligned} &m = 3\ &(x_1, y_1) = (-1, -7) \end{aligned} $$ ## Write the equation of the line Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &y - y_1 = m(x - x_1)\ &y - (-7) = 3(x - (-1))\ &y + 7 = 3(x + 1) \end{aligned} $$ ## Solve for the y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y + 7 = 3x + 3\ &y = 3x + 3 - 7\ &y = 3x - 4\ &b = -4 \end{aligned} $$

(A) $-10$

(B) $-4$

(C) $3$

(D) $7$

{ "elements": [ { "type": "point", "params": [[-1, -7]], "properties": { "name": "(-1, -7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, -4]], "properties": { "name": "(0, -4)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "3*x - 4", "latex": "y = 3x - 4"}, -3, 3], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 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 values

Write the equation of the line

Solve for the y-intercept

Answer: