Equation of a straight line

Geometry Level 2

Find the equation of the line that passes through the points ( 3 , − 10 ) (3,-10) and ( − 2 , 5 ) (-2,5) . If your answer is in the form y = m x + b y = mx + b , give your answer as m + b m + b .

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The answer is -4.

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1 solution

Find the slope,m.

m = y 2 − y 1 x 2 − x 1 = 5 + 10 − 2 − 3 = 15 − 5 = − 3 m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 + 10}{-2 - 3} = \frac{15}{-5} = -3

From point-slope intercept form of an equation of a line using the point ( 3 , − 10 ) (3,-10) , we have

y − y 1 = m ( x − x 1 ) y - y_1 = m(x - x_1)

y + 10 = − 3 ( x − 3 ) y + 10 = -3(x - 3) ⟹ \implies y + 10 = − 3 x + 9 y+10=-3x+9 ⟹ \implies y = − 3 x − 1 \boxed{\color{#20A900}y=-3x-1}

Finally,

m + b = − 3 + − ( 1 ) = m + b = -3 + -(1) = − 4 \boxed{\color{#3D99F6}-4}

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Please can you add a Arabic version of the questions because it's getting hard to translate.

Thanks, Mostafa

mostafa ahmed - 2 years, 5 months ago

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