Find the gradient of the straight line that passes through the points (3,6) and (-5,-2) and hence find the equation of the line, clearly showing each step of your method
points (3,6) and (-5,-2)
Slope m = (y2 - y1)/(x2 - x1)
m = (-2 - 6)/(-5 - 3)
m = -8/-8 = 1
Slope-intercept form of the equation,
y = mx + b,
where m = slope and b = y-intercept
To find the y-intercept, Use either point to substitute into the equation,
y = mx + b
P (3,6), m = 1
y = mx + b
6 = 1(3) + b
6 = 3 + b
b = 3
Therefore, the equation where m = 1 and b = 3 is,
y = 1x + 3
y = x + 3
To find the gradient of the straight line that passes through two points, (x1, y1) and (x2, y2), we can use the formula:
Gradient (m) = (y2 - y1) / (x2 - x1)
In this case, the two points are (3, 6) and (-5, -2).
Step 1: Identify the coordinates
x1 = 3
y1 = 6
x2 = -5
y2 = -2
Step 2: Plug the values into the gradient formula
m = (-2 - 6) / (-5 - 3)
= -8 / -8
= 1
The gradient of the line is 1.
Now, let's find the equation of the line using the point-slope form:
y - y1 = m(x - x1)
Step 3: Choose one of the points and plug in the values
Using the point (3, 6):
y - 6 = 1(x - 3)
Step 4: Simplify the equation
y - 6 = x - 3
Step 5: Rearrange the equation to get the standard form
y = x - 3 + 6
y = x + 3
Hence, the equation of the line is y = x + 3.
Thanks! I'm covering maths classes so it's annoying not knowing how to explain and mark work
we are trying to find out how to use the equation to determine whether or not the point (-3,2) lies on this line?
the x-intercept and the y-intercept of the line in the first question and the kids have to show each step of their method clearly.