how do i find the equation for the lines:
1. y-intercept of -2.1, x-intercept of 3.5
2. through (1.2,5.1), x-intercept of 3.7
In factored form:
y=a(x-á)(x-â)
The alpha and beta symbols are the x-intercepts (or roots). If you plug in the x-inercept, and then the point that you know, you can find the value of 'a' and thus form an equation.
For your first one:
sub in the root
y=a(x-(3.5))
sub in the point
-2.1=a(0-3.5)
-2.1=a(-3.5)
a=0.6
Therefore: y=0.6(x-3.5)
I apologize, the alpha and beta symbols didn't show up. The a's with accents over them are the roots.
As well, I made a mistake in the final equation (forgot a letter).
y=0.6x(x-3.5)
1. y = 0 at the x-int.
x = 0 at the y -jnt.
(0 , -2.1), (3.5 , 0),
Slope = ((0 - (-2.1)) / (3.5 - 0) = 3/5
y = mx + b,
-2.1 = (3/5)*0 + b,
b = -2.1,
Eq: y = (3/5)x - 2.1.
2. (1.2 , 5.1) , (3.7 , 0),
Slope = (0 - 5.1) / (3.7 - 1.2) =
-5.1/2.5 = -2.04,
y = mx + b,
5.1 = -2.04*1.2 + b,
5.1 = -2.45 + b,
b = 5.1 + 2.45 = 7.55,
Eq: y = -2.04x + 7.55.
through (3.5, -2.3), x-intercept 5.1
To find the equation for a line, you can use the slope-intercept form, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
1. Finding the equation for a line with a y-intercept of -2.1 and an x-intercept of 3.5:
To find the slope (m), you can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. In this case, the y-intercept is (0, -2.1) and the x-intercept is (3.5, 0).
m = (-2.1 - 0) / (0 - 3.5)
= -2.1 / -3.5
= 0.6
Now that we know the slope (m) is 0.6, we can use the y-intercept (-2.1) to write the equation:
y = 0.6x - 2.1
2. Finding the equation for a line through the point (1.2, 5.1) and with an x-intercept of 3.7:
Again, we can use the slope-intercept form (y = mx + b).
To find the slope (m), we will use the formula:
m = (y2 - y1) / (x2 - x1)
= (0 - 5.1) / (3.7 - 1.2)
= -5.1 / 2.5
= -2.04
Now that we know the slope (m) is -2.04, we can use the point (1.2, 5.1) to write the equation:
y = -2.04x + b
To find the value of b (the y-intercept), we substitute the coordinates of the given point into the equation:
5.1 = -2.04(1.2) + b
5.1 = -2.448 + b
b = 5.1 + 2.448
b = 7.548
Therefore, the equation of the line is:
y = -2.04x + 7.548