Find an equation of the line containing the points (-6,19) and (-15,28)
Thanks a bunch
Why did the line cross the road? Because it couldn't decide between (-6,19) and (-15,28) and wanted to explore both points!
But if you're looking for an equation, we can use the point-slope formula!
The formula is: y - y1 = m(x - x1)
First, let's find the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1)
m = (28 - 19) / (-15 - (-6))
m = 9 / -9
m = -1
Now, let's choose a point. How about (-6,19)?
Using the point-slope formula, the equation would be:
y - 19 = -1(x - (-6))
Simplifying this equation, we get:
y - 19 = -1(x + 6)
y - 19 = -x - 6
y = -x + 13
So, the equation of the line passing through (-6,19) and (-15,28) is y = -x + 13.
To find the equation of a line passing through two given points, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Calculate the slope (m)
The formula for calculating the slope between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using the given points (-6,19) and (-15,28), we can substitute the values into the formula:
m = (28 - 19) / (-15 - (-6))
= 9 / (-15 + 6)
= 9 / -9
= -1
So, the slope (m) of the line is -1.
Step 2: Find the y-intercept (b)
To find the y-intercept, we can choose any point on the line and substitute its coordinates into the equation y = mx + b. Let's choose the point (-6, 19):
19 = -1 * (-6) + b
19 = 6 + b
b = 19 - 6
b = 13
Therefore, the y-intercept (b) is 13.
Step 3: Write the equation
Now that we have the slope (m = -1) and the y-intercept (b = 13), we can write the equation of the line:
y = mx + b
y = -x + 13
Hence, the equation of the line passing through the points (-6,19) and (-15,28) is y = -x + 13.
Hello, find the slope first using the Slope Formula: Y2-Y1/X2-X1
X1=-6
Y1=19
X2=-15
Y2=28
28-19/-15-(-6)
9/-15+6
9/-9
-1
The slope is -1, now use point slope form to determine the equation of the line.
Y2-Y1= M(X2-X1)
M= Slope
X and Y are coordinates above
Y-19= -1(X-(-6)
Y-19=-1(X + 6)
Y-19= -X-6
Y= -X- 6 + 19
y= -X + 13
Hope this helps!