1)FInd an equation of the line containting the given pair of points.
(-8,0) and (0,5)
MY ANSWEAR: (5/8)X+5
2)Find an equation of the line having the given slope and containing the given point.
m=6 (8,1)
MY ANSWEAR: 6X-47
1)
Firstly we need to find the slope of the line the two points are on by using the equation
m = (y2-y1)/(x2-x1)
m = (5 - 0)/(0 - [-8]) = 5/(0 + 8)
m = 5/8
Then use y-y1=m(x-x1) to find the equation of the line.
y - 0 = (5/8)*(x - [-8])
y = 5/8x + 5
So your answer is correct :)
2)
You can jump straight to the
y-y1=m(x-x1) equation.
y - 1 = 6(x - 8)
y - 1 = 6x - 48
y = 6x - 48 + 1
y = 6x - 47
So you got both parts correct :)
Well done!
To find the equation of a line, we need to use the slope-intercept form of a line, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
1) To determine the slope (m) of the line passing through the points (-8, 0) and (0, 5), we use the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the formula, we have: m = (5 - 0)/(0 - (-8)) = 5/8.
Now that we have the slope, we can use one of the given points (-8, 0) and the slope (5/8) to find the y-intercept (b).
Using the slope-intercept form, we substitute the values of x, y, and m into the equation: 0 = (5/8)(-8) + b.
Simplifying the equation, we get: 0 = -5 + b.
Solving for b, we find: b = 5.
Therefore, the equation of the line passing through the points (-8, 0) and (0, 5) is y = (5/8)x + 5.
2) Given a slope (m) of 6 and a point (8, 1), we can directly substitute the values into the slope-intercept form of a line.
Using the equation y = mx + b, we substitute the slope (m) and the coordinates of the point (x, y) into the equation: 1 = 6(8) + b.
Simplifying the equation, we get: 1 = 48 + b.
Solving for b, we find: b = -47.
Therefore, the equation of the line with a slope of 6 passing through the point (8, 1) is y = 6x - 47.