25JUL21










 

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17JUL21

Ax+By+C=0 Does this represent a straight line? Yes, it does because it is a "LINEAR" equation in x and y. (The power of x is 1 and the power of y is 1.) What is the slope of this line? What is the y-intercept of this line? And what is the x-intercept? By = -Ax-C y = (-Ax-C)/B y = (-Ax/B) - (C/B) y = (-A/B)x - (C/B) Compare this to y = mx+c m = -A/B c = C/B Therefore, Ax+By+C=0 has a slope of -A/B. Its y-intercept is -C/B. It cuts the Y-Axis at the point (0, -C/B). To find the x-intercept, we have to substitute 0 for y. Ax+By+C=0 Ax+B(0)+C=0 Ax+C=0 Ax=-C x = -C/A So the x-intercept is -C/A. That is, Ax+By+C=0 cuts the X-Axis at the point (-C/A,0). Summary: Ax+By+C=0, Slope=-A/B, y-intercept=-C/B, x-intercept=-C/A What is the slope of any line parallel to Ax+By+C=0? -A/B What is the slope of any line perpendicular to Ax+By+C=0? Let us say the slope of the perpendicular line is p. (-A/B)p=-1 p=(-1)(-B/A) p=B/A Analyse 2x+3y+4=0. [Comparing with Ax+By+C=0, A=2, B=3 and C=4.] 01) ...
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13JUL21

Given the equation of a line, to find its slope, compare the given equation to y=mx+c. Whatever is the coefficient of x, it is the slope of the line. In the given equation, if the LHS is not y, you have to modify the given equation and bring it into the form y=mx+c. Given the equation of a line, to find its y-intercept, compare the given equation to y=mx+c. Whatever is the constant term, it is the y-intercept made by the line. Alternatively, we can substitute 0 for x, because any point on the Y-Axis will have its x-coordinate as zero. Given the equation of a line, to find its x-intercept, we can substitute 0 for y, because any point on the X-Axis will have its y-coordinate as zero. y=mx+c is called the slope-intercept form of a straight line. +a in the LHS becomes –a in the RHS. –a in the LHS becomes +a in the RHS. *a in the LHS becomes /a in the RHS. /a in the LHS becomes *a in the RHS.
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20JUL21

What is the slope of (x/2) + (y/3) = 1? 3/2 Does this line make an acute angle with the X-Axis or obtuse? Obtuse Does the point (1,3/2) lie on this line? (x/2)+(y/3)=1 (1/2)+(3/2 divided by 3)=1 (1/2)+(1/2)=1 1=1 LHS=RHS Yes, the point lies on the line.
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