find an equation of the line having the given slope and containing the given point express your answer in the form x=a,y=b,ory=mx+b m=-2,(5,0)
Do not understand this question.
The usual equation of a straight line with a know slope is
y = mx + b
where m is the slope, and
b is the y-intercept.
The question provides you with the slope m=2 and a point P(5,0) through which the line passes.
The equation of a line passing through a point P1(x1,y1) with a slope of m is
(y-y1)=m(x-x1)
In effect, what you are required to do is to substitute the given values of m and (x1,y1) into the above equation, and simplify the resulting equation into the form y=mx+b.
Unfortunately the form of the equation y=mx+b does not work when the line is parallel to the y-axis when the equation takes the form x=a, or when the line is parallel to the x-axis, then it takes the form y=b, where a and b are the x and y-intercepts respectively.
Give the problem a try and post your answer for verification if necessary.
To find the equation of a line given its slope and a point it passes through, you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of the given point, and m is the slope.
In this case, the given point is (5, 0) and the slope is -2.
Substituting these values into the point-slope form equation:
y - 0 = -2(x - 5)
Simplifying:
y = -2(x - 5)
Now, we can expand and rewrite the equation in the desired format:
y = -2x + 10
So, the equation of the line with a slope of -2 and passing through the point (5, 0) is y = -2x + 10.