graph the following linear equation.

\y = -2x + 7\

step 3 of 3: plot a second point on the graph (other than the $y$-intercept) such that the slope of the line connecting the point and the $y$-intercept is equal to the slope of the given equation.

Question

graph the following linear equation.

\y = -2x + 7\

step 3 of 3: plot a second point on the graph (other than the $y$-intercept) such that the slope of the line connecting the point and the $y$-intercept is equal to the slope of the given equation.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Plotting Points" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Plotting Points", "Graphing Linear Equations" ] } ## Identify the slope and y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b \ &y = -2x + 7 \ &m = -2, \quad b = 7 \implies (0, 7) \end{aligned} $$ ## Find a second point using the slope Using the *Plotting Points* knowledge point $$ \begin{aligned} &m = \frac{\Delta y}{\Delta x} = \frac{-2}{1} \ &(x_1, y_1) = (0 + 1, 7 - 2) = (1, 5) \end{aligned} $$ Plot the second point at $(1, 5)$. { "elements": [ { "type": "point", "params": [[0, 7]], "properties": { "name": "y-intercept (0, 7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 5]], "properties": { "name": "Second Point (1, 5)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "line", "params": [[0, 7], [1, 5]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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Question

Explanation:

Identify the slope and y-intercept

Find a second point using the slope

Answer: