find an equation for the line that passes through (-4, 8) and (3, -7). what is the slope? where does the line intersect the x-axis and the y-axis?

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12-07-2016
Mathematics

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find an equation for the line that passes through (-4, 8) and (3, -7). what is the slope? where does the line intersect the x-axis and the y-axis?

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dalendrk dalendrk · Answer 1 · 2016-07-16T22:17:44+02:00

[tex](x_1;\ y_1);\ (x_2;\ y_2)\\\\the\ slope:m=\dfrac{y_2-y_1}{x_2-x_1}\\\\the\ slope\ form\ of\ the\ line:y=mx+b\\the\ point-slope\ form:y-y_1=m(x-x_1)\\-------------------\\\\(-4;\ 8)\to x_1=-4;\ y_1=8\\(3;-7)\to x_2=3;\ y_2=-7\\\\m=\dfrac{-7-8}{3-(-4)}=\dfrac{-15}{3+4}=-\dfrac{15}{7}\\\\\\y-8=-\dfrac{15}{7}(x-(-4))\\\\y-8=-\dfrac{15}{7}x-\dfrac{60}{7}\\\\y=-\dfrac{15}{7}x-\dfrac{4}{7}\\\\x-intercept\ when\ y=0\\-\dfrac{15}{7}x-\dfrac{4}{7}=0\ \ \ |\cdot7\\\\-15x-4=0\ \ \ |+4\\\\-15x=4\ \ \ |:(-15)[/tex]

[tex]x=-\dfrac{4}{15}\to\left(-\dfrac{4}{15};\ 0\right)\\\\y-intrcept\ when\ x=0\\\\y=-\dfrac{15}{7}\cdot0-\dfrac{4}{7}\\\\y=-\dfrac{4}{7}\to\left(0;-\dfrac{4}{7}\right)[/tex]