graph the following linear equation.

\y = \frac{-2}{5}x + 4\

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 = \frac{-2}{5}x + 4\

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", "Cartesian Coordinates" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Plotting Points", "Cartesian Coordinates", "Coordinate Geometry" ] } ## Identify the slope and y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b \ &y = \frac{-2}{5}x + 4 \ &m = -\frac{2}{5}, \quad b = 4 \implies (0, 4) \end{aligned} $$ ## Apply slope to find a second point Using the *Plotting Points* and *Cartesian Coordinates* knowledge points $$ \begin{aligned} &\text{Slope } m = \frac{\text{rise}}{\text{run}} = \frac{-2}{5} \ &(x_1, y_1) = (0 + 5, 4 - 2) = (5, 2) \ &(x_2, y_2) = (0 - 5, 4 + 2) = (-5, 6) \end{aligned} $$ A second point to plot on the graph is $(5, 2)$ (or alternatively $(-5, 6)$). { "elements": [ { "type": "point", "params": [[0, 4]], "properties": { "name": "y-intercept (0, 4)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 2]], "properties": { "name": "Second Point (5, 2)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "line", "params": [[0, 4], [5, 2]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the slope and y-intercept

Apply slope to find a second point

Answer: