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Parthyy
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A STRAIGHT LINE has equation y=2x+1. The point coordinates (0,a) , (b,0) , (2,d) and (e,7) lie on this line. Find the values of a,b,d, and e.
You have an equation y = 2x + 1 and several ordered pairs on that line.Parthyy said:A STRAIGHT LINE has equation y=2x+1. The point coordinates (0,a) , (b,0) , (2,d) and (e,7) lie on this line. Find the values of a,b,d, and e.
Each pair represents (x, y). The line is given as y= 2x+ 1 so (0, a) must satisy a= 2(0)+ 1. similarly, (b, 0) must satisfy 0= 2b+ 1. Solve that equation for b. (2, d) must satisfy d= 2(2)+ 1. (e, 7) must satisfy 7= 2e+ 1. Solve that equation for e.Parthyy said:A STRAIGHT LINE has equation y=2x+1. The point coordinates (0,a) , (b,0) , (2,d) and (e,7) lie on this line. Find the values of a,b,d, and e.
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. To find the equation of the line passing through (0,a) and (b,0), we need to first find the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (0 - a) / (b - 0) = -a/b. Now, we can use the slope-intercept form to write the equation as y = -a/b * x + b. To find the value of b, we can substitute one of the given points and solve for b. For example, using (0,a), we get a = -a/b * 0 + b, which simplifies to b = a. Therefore, the equation of the line is y = -a/b * x + a.
Since both points lie on the same line, we can substitute their coordinates into the equation y = 2x + 1 and solve for a. Using (0,a), we get a = 2 * 0 + 1 = 1. Therefore, the value of a is 1.
Similar to the previous question, we can substitute the coordinates into the equation y = 2x + 1 and solve for b. Using (b,0), we get 0 = 2 * b + 1, which simplifies to b = -1/2. Therefore, the value of b is -1/2.
Yes, the point (e,7) can lie on the line y = 2x + 1 if e is a positive integer. To prove this, we can substitute the coordinates into the equation and solve for e. Using (e,7), we get 7 = 2 * e + 1, which simplifies to e = 3. Therefore, if e is a positive integer, the point (e,7) can lie on the line y = 2x + 1.
Similar to the previous questions, we can substitute the coordinates into the equation y = 2x + 1 and solve for d. Using (2,d), we get d = 2 * 2 + 1 = 5. Therefore, the value of d is 5.