The equation of the line with x-intercept 2 and y-intercept 1 can be written in the form y= mx+b where
The number m is :
The number b is:
To find the equation of the line with x-intercept 2 and y-intercept 1 in the form y= mx+b, we need to determine the values of m and b.
The x-intercept is the point where the line crosses the x-axis. Given that the x-intercept is 2, this means that when y=0, x=2.
The y-intercept is the point where the line crosses the y-axis. Given that the y-intercept is 1, this means that when x=0, y=1.
We can use these two points (2, 0) and (0, 1) to find the slope of the line (m). The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the two points:
m = (0 - 1) / (2 - 0) = -1/2
So the value of m is -1/2.
To find the value of b, we can substitute the coordinates of one of the points (2, 0) into the equation y = mx + b and solve for b:
0 = (-1/2)(2) + b
0 = -1 + b
b = 1
So the value of b is 1.
Therefore, the equation of the line with x-intercept 2 and y-intercept 1 in the form y = mx + b is y = -1/2x + 1.
To determine the equation of a line with given x-intercept and y-intercept, we can use the intercept form of a linear equation, which is:
x/a + y/b = 1
where a is the x-intercept and b is the y-intercept.
Given that the x-intercept is 2 and the y-intercept is 1, we can substitute these values into the equation:
x/2 + y/1 = 1
Now, let's simplify the equation and rewrite it in the form y = mx + b:
x/2 + y = 1
Multiply through by 2 to eliminate the fraction:
2(x/2) + 2y = 2
Simplify:
x + 2y = 2
To write this equation in the form y = mx + b, we need to solve for y. Let's isolate y:
2y = -x + 2
Divide through by 2:
y = (-1/2)x + 1
Now we can identify the values of m and b in the equation y = mx + b:
m = -1/2
b = 1
Therefore, the equation of the line with x-intercept 2 and y-intercept 1 in the form y = mx + b is: y = (-1/2)x + 1.
x-intercept 2 and y-intercept 1
implies you have the two points (2,0) and (0,1)
slope = (1-0)/(0-2) = -1/2
y = (-1/2)x + 1
what are your thoughts ?
or, start with the intercept form of the line:
x/2 + y/1 = 1