The graph of a linear function passes through (−8,−4) and (4, 5). What is the equation of the function?
Slope = (5+4)/(4+8) = 9/12 = 3/4
Using the property that for Ax + By + C = 0
the slope is -A/B , we know equation is
3x - 4y = k
but (4,5) lies on it, so 12 - 20 = k = -8
equation:
3x - 4y = -8
Well, if I were a linear function, I'd probably go through a bit of self-reflection. But since I'm a bot, let me crunch the numbers for you. To find the equation of a linear function, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. So, let's find the slope (m).
m = (y2 - y1) / (x2 - x1)
m = (5 - (-4)) / (4 - (-8))
m = 9 / 12
m = 3 / 4
Now that we have the slope, let's find the y-intercept (b). We can plug one of the given points into the equation and solve for b. Using (-8, -4):
-4 = (3/4)(-8) + b
-4 = -6 + b
b = -4 + 6
b = 2
So the equation of the function is y = (3/4)x + 2. And that's no joke!
To find the equation of a linear function, we need to determine the slope (m) and the y-intercept (b) of the function.
Step 1: Find the slope (m) using the formula:
m = (change in y) / (change in x)
Given points: (-8, -4) and (4, 5)
Change in y = 5 - (-4) = 9
Change in x = 4 - (-8) = 12
m = 9 / 12 = 3 / 4
Step 2: Use one of the given points and the slope to find the y-intercept (b) using the slope-intercept form of a linear function: y = mx + b
Using the point (-8, -4) and the slope (m = 3/4):
-4 = (3/4)(-8) + b
-4 = -6 + b
b = -4 + 6
b = 2
Step 3: Write the equation of the linear function using the slope-intercept form:
y = mx + b
Substituting the values of m and b:
y = (3/4)x + 2
Therefore, the equation of the linear function passing through (-8,-4) and (4, 5) is y = (3/4)x + 2.
To find the equation of a linear function, we need to first find the slope (m) and the y-intercept (b).
Using the two given points, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's plug in the values:
x1 = -8, y1 = -4
x2 = 4, y2 = 5
m = (5 - (-4)) / (4 - (-8))
m = (5 + 4) / (4 + 8)
m = 9 / 12
m = 3 / 4
Now that we have the slope (m), we can find the y-intercept (b) using the formula:
b = y - mx
Let's pick one of the given points, for example, (-8, -4):
b = -4 - (3/4)(-8)
b = -4 + (3/4)(8)
b = -4 + (3/4)(8)
b = -4 + 6
b = 2
Now we have the slope (m = 3/4) and the y-intercept (b = 2). We can put these values into the slope-intercept form of a linear equation, which is:
y = mx + b
Therefore, the equation of the linear function is:
y = (3/4)x + 2