Can someone help me plwease with this problem????? I need to find an equation for the given pair of points and express my answer in x=a,y=b, or y=mx+b form. Please explain it simply as I am really struggling with this.
(-1,-1) and (6,6). Thank you so much for your help!!!!!
(-1 ,-1) , (6 , 6)
Slope = (6 - (-1)) / (6 - (-1)) =
7 /7 = 1,
y = mx + b,
-1 = 1 * -1 + b,
b = 0
Eq: y = 1x + 0,
y = x.
Of course, I can help you with that! To find the equation of a line in the form of y = mx + b, we need to determine the values of m (slope) and b (y-intercept). Here's how you can do it step by step:
Step 1: Determine the slope (m)
The formula for slope (m) is: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points.
For the points (-1,-1) and (6,6), we can label them as: (x1, y1) = (-1, -1) and (x2, y2) = (6, 6).
Now, substitute the values into the slope formula:
m = (6 - (-1)) / (6 - (-1))
Step 2: Calculate the slope (m)
Simplifying the equation gives us:
m = (6 + 1) / (6 + 1)
m = 7 / 7
m = 1
Therefore, the slope of the line passing through those two points is 1.
Step 3: Determine the y-intercept (b)
To find the y-intercept (b), we can use the slope-intercept form of a line equation: y = mx + b. Plugging in one of the points, (-1,-1), we can solve for b.
Using the point (-1,-1) and the slope (m = 1):
-1 = 1 * (-1) + b
Simplifying the equation:
-1 = -1 + b
Now, solve for b:
b = -1 + 1
b = 0
Therefore, the y-intercept (b) is 0.
Step 4: Write the equation
Now that we have the slope (m = 1) and y-intercept (b = 0), we can write the equation in slope-intercept form, y = mx + b.
Plugging in the values:
y = 1x + 0
y = x
So, the equation of the line passing through the points (-1,-1) and (6,6) is y = x.
I hope this explanation helps you understand the steps involved in finding the equation of a line using two given points and expressing it in y = mx + b form.