Find the slope, x-intercept, and y-intercept for the line 9 x + 10 y + 16 = 0 I found y to be -1.6, the slope to be -.9 and x to be wither 0/9 or -16 but it said i got x wrong
here is a nice way to find the x and y intercepts if the equation is written in the general form such as 9x + 10y + 16 = 0
move the constant to the right side :
9x + 10y = - 16
now for the x-intercept, let y = 0
Put your pencil or your pinkie finger over the y term to block it out
you should now see 9x = -10
and in your head you should be able to get x = -10/9 or
do the same thing for the y-intercept to get y = -16/10 = -1.6 (which yougot)
Also for Ax + By + C = 0 the slope is -A/B
so in our case the slope = -9/10
the long way of course is to change it to the form y = mx + b
9x + 10y + 16 = 0
10y = -9x - 16
y = (-9/10)x - 16/10
so m = -9/10
To find the slope, x-intercept, and y-intercept of the line 9x + 10y + 16 = 0, let's start by rearranging the equation in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Subtract 9x from both sides of the equation to isolate the y term:
10y = -9x - 16
Step 2: Divide the entire equation by 10 to solve for y:
y = (-9/10)x - (16/10)
y = (-9/10)x - 8/5
From this equation, we can see that the slope (m) is -9/10.
Step 3: To find the x-intercept, set y = 0 and solve for x:
0 = (-9/10)x - 8/5
Multiply the entire equation by -10 to eliminate the denominator:
0 = 9x + 16
Now, solve for x:
9x = -16
x = -16/9
Therefore, the x-intercept is -16/9.
Step 4: To find the y-intercept, set x = 0 and solve for y:
y = (-9/10)(0) - 8/5
y = -8/5
Therefore, the y-intercept is -8/5.
To summarize:
Slope: -9/10
X-intercept: -16/9
Y-intercept: -8/5
To find the slope, x-intercept, and y-intercept for the given line equation, we need to rewrite the equation in the slope-intercept form: y = mx + c, where m represents the slope, and c represents the y-intercept.
Starting with the given equation: 9x + 10y + 16 = 0, let's isolate y by subtracting 9x and 16 from both sides:
10y = -9x - 16
Divide both sides by 10 to solve for y:
y = (-9/10)x - (16/10)
y = (-9/10)x - 8/5
Now we can see that the coefficient of x, -9/10, represents the slope of the line. Therefore, the slope is -9/10.
To find the x-intercept, we set y = 0 and solve for x:
0 = (-9/10)x - 8/5
Multiply both sides by 10 to eliminate the fraction:
0 = -9x - 16
Add 16 to both sides:
9x = -16
Divide by 9 to solve for x:
x = -16/9
Therefore, the x-intercept is -16/9.
To find the y-intercept, we set x = 0 and solve for y:
y = (-9/10)(0) - 8/5
y = -8/5
So, the y-intercept is -8/5.
In summary:
- The slope of the line is -9/10.
- The x-intercept is -16/9.
- The y-intercept is -8/5.