What is the y-intercept of the line that passes through the points (2,-1) and (-3,9)
1 answer:
Answer:
<em>The equation of the straight line y = -2x +3</em>
<em>y-intercept = 3 and m =-2</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the points are ( 2,-1) and (-3,9)
The slope of the line
<u><em>Step(ii):</em></u>-
The equation of the straight line passing through the point ( 2,-1) and slope m=-2
y-y₁ = m( x- x₁)
y -(-1) = -2 ( x-2)
y +1 = -2x +4
2x +y +1-4 =0
2x +y -3 =0
<u><em>Final answer:-</em></u>
<em>The equation of the straight line y = -2x +3</em>
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The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
<h3>How to determine the legs of the triangle?</h3>The complete question is in the attached image
The given parameters are:
Area = 24
Legs = x and x + 2
The area of the triangle is calculated as:
Area = 0.5 * Base * Height
This gives
0.5 * x * (x + 2) = 24
So, we have:
0.5(x)(x + 2) = 24
Divide through by 0.5
(x)(x + 2) = 48
Expand
x^2 + 2x = 48
Subtract 48 from both side
x^2 + 2x - 48 = 0
Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
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