given two points one a line (8,1) and 10,8) find the x intercept and y intercept
PLEASE HELP!
slope is 7/7 = 1
so the equation is y = x+b
but (8,1) lies on it, so
1 = 8 + b
b = -7
your equation is y = x - 7
clearly the y-intercept is -7 by the definition of y = mx + b
for the x-intercept, let y=0 and solve for x
when i did it i got the slope=7/2
how did you get 7/7?
you are absolutely right, my mental arithmetic is often pathetic.
so just follow the rest of my solution with a slope of 7/2
did you get y-intercept of -27 and
x-intercept of 54/7 ?
yes i did!
thanks so so much
564
To find the x-intercept and y-intercept of a line given two points, you can use the slope-intercept form of a linear equation, which is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept.
First, let's find the slope (m) using the two given points (8,1) and (10,8). The slope can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points:
m = (8 - 1) / (10 - 8)
m = 7 / 2
Next, substitute one of the points into the slope-intercept equation (y = mx + b) to find the y-intercept (b). Let's use the first point (8,1):
1 = (7/2) * 8 + b
Simplify the equation:
1 = 28 + b
Since we want to solve for b, isolate it:
b = 1 - 28
b = -27
Therefore, the equation of the line in slope-intercept form is: y = (7/2)x - 27.
To find the x-intercept, set y equal to zero in the equation y = (7/2)x - 27 and solve for x:
0 = (7/2)x - 27
Add 27 to both sides:
27 = (7/2)x
To isolate x, multiply both sides by 2/7:
2/7 * 27 = x
x = 54/7
So, the x-intercept is (54/7, 0).
To find the y-intercept, set x equal to zero in the equation y = (7/2)x - 27:
y = (7/2) * 0 - 27
y = -27
So, the y-intercept is (0, -27).