The equations are 6.5x + 8.3y + 7.1 = 0 and
-7.2x + 3.4y - 6.6 = 0. Find the slope and x and y intercepts of each equation.
For the first equation I got the x intercept as -10.92 and y intercept as -8.55 but I can't figure out the slope.
For the second one i got the x as -.915 and y as 1.94. but i can't get the slope either.
To find the slope and intercepts of each equation, we need to manipulate the equations into the standard form, which is Ax + By + C = 0, where A, B, and C are constants.
Let's start with the first equation: 6.5x + 8.3y + 7.1 = 0
To find the x-intercept, we set y = 0 and solve for x:
6.5x + 8.3(0) + 7.1 = 0
6.5x + 7.1 = 0
6.5x = -7.1
x = -7.1 / 6.5
x ≈ -1.092
So, the x-intercept is approximately -1.092.
To find the y-intercept, we set x = 0 and solve for y:
6.5(0) + 8.3y + 7.1 = 0
8.3y + 7.1 = 0
8.3y = -7.1
y = -7.1 / 8.3
y ≈ -0.855
So, the y-intercept is approximately -0.855.
Now, to find the slope, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope.
6.5x + 8.3y + 7.1 = 0
8.3y = -6.5x - 7.1
y = (-6.5/8.3)x - 7.1/8.3
So, the slope of the first equation is approximately -6.5/8.3.
Now let's move on to the second equation: -7.2x + 3.4y - 6.6 = 0
To find the x-intercept, we set y = 0 and solve for x:
-7.2x + 3.4(0) - 6.6 = 0
-7.2x - 6.6 = 0
-7.2x = 6.6
x = 6.6 / -7.2
x ≈ -0.915
So, the x-intercept is approximately -0.915.
To find the y-intercept, we set x = 0 and solve for y:
-7.2(0) + 3.4y - 6.6 = 0
3.4y - 6.6 = 0
3.4y = 6.6
y = 6.6 / 3.4
y ≈ 1.941
So, the y-intercept is approximately 1.941.
Now, to find the slope, we again need to rewrite the equation in slope-intercept form:
-7.2x + 3.4y - 6.6 = 0
3.4y = 7.2x + 6.6
y = (7.2/3.4)x + 6.6/3.4
So, the slope of the second equation is approximately 7.2/3.4.
Therefore, for the first equation:
- x-intercept ≈ -1.092
- y-intercept ≈ -0.855
- slope ≈ -6.5/8.3
For the second equation:
- x-intercept ≈ -0.915
- y-intercept ≈ 1.941
- slope ≈ 7.2/3.4