correct me if I'm wrong please.
7. what is the equation of the line which passes through c(2,3) and has a slope m =1/2?
a.)x-2y=-4 <<<<< my choice
b.)2x-y =1
c.)2x+y=7
d.)x+2y=8
what is the equation of the line which passes through point d(-4,2) and has angle of inclination 0=60degrees? leave all decimal places in the result.
a.)0.8660x-y=-5.46412
b.)1.73205x-y = -8.9282 <<<
c.)x - 0.86603y =5.73206
d.) x -1.73205y = -7.4641
For the first question, you are given the slope of the line, which is 1/2, and a point on the line, which is c(2,3). To find the equation of the line, you can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get: y - 3 = (1/2)(x - 2).
To simplify this equation, distribute the 1/2 to the terms inside the parentheses: y - 3 = (1/2)x - 1.
Now, isolate the y-term by subtracting 1/2x from both sides of the equation: y = (1/2)x + 2.
So, the equation of the line passing through point c(2,3) with a slope of 1/2 is y = (1/2)x + 2.
For the second question, you are given a point on the line, which is d(-4,2), and an angle of inclination of 60 degrees. The angle of inclination is the angle formed between the positive x-axis and the line.
To find the equation of the line, we need to convert the angle of inclination into the slope of the line. The slope is defined as the tangent of the angle of inclination. So, the slope (m) is the tangent of 60 degrees, which is sqrt(3) or approximately 1.73205.
Using the point-slope form of a line, we can write the equation as: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get: y - 2 = 1.73205(x + 4).
Simplifying the equation, distribute the 1.73205 to the terms inside the parentheses: y - 2 = 1.73205x + 6.9282.
Isolate the y-term by subtracting 1.73205x from both sides of the equation: -1.73205x + y = 8.9282.
Thus, the correct answer is b.) 1.73205x - y = -8.9282.