Dans cette question, il s'agit de trouver une équation de droite de la forme $y=mx+c$ passant par deux points dont les coordonnées sont données.
\n", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variable_groups": [], "ungrouped_variables": ["x_a", "x_b", "y_a", "y_b", "m", "c"], "advice": "L'équation d'une droite passant par deux points se trouve en calculant le coefficient directeur de la droite et l'ordonnée à l'origine.
\nOn trouve le coefficient directeur ($m$) en utiliant les points $A = (x_1,y_1)=(\\var{x_a},\\var{y_a})$ et $B = (x_2,y_2)=(\\var{x_b},\\var{y_b})$ grâce à la formule suivante :
\n\\begin{align}
m &= \\frac{y_2-y_1}{x_2-x_1} \\\\[0.5em]
&= \\frac{\\simplify[!collectNumbers]{{y_b}-{y_a}}}{\\simplify[!collectNumbers]{{x_b}-{x_a}}} \\\\[0.5em]
&= \\frac{\\simplify[]{{y_b}-{y_a}}}{\\simplify{{x_b}-{x_a}}} \\\\[0.5em]
&= \\simplify[simplifyFractions,unitDenominator]{({y_b-y_a})/({x_b-x_a})}\\text{.}
\\end{align}
L'équation de la droite étant de la forme $y=mx+c$, on trouve l'ordonnée à l'origine $c$ en utiisant les coordonnées d'un des deux points :
\n\\[c = y_1-mx_1 \\quad \\mathrm{ou} \\quad c = y_2-mx_2 \\,\\text{.} \\]
\nPar exemple avec le point $A$ :
\n\\[
\\begin{align}
c &= y_1-mx_1 \\\\
&= \\var{y_a}-\\var[fractionnumbers]{m}\\times\\var{x_a} \\\\
& = \\simplify[fractionnumbers]{{y_a-m*x_a}}\\text{.}
\\end{align}
\\]
c)
\nOn injecte alors les valeurs calculées de $m$ et $c$ dans l'équation $y=mx+c$ et on obtient l'équation de droite:
\n\\[y=\\simplify[!noLeadingMinus,fractionNumbers,unitFactor]{{m} x+ {c}}\\text{.}\\]
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\n$\\displaystyle y=$ [[0]]
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