Write an equation for the line with points (4,5) and (6,9).
Please explain.
To write an equation for the line passing through two points, we can use the formula for the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.
Step 1: Find the slope (m)
The formula to calculate the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using the given points (4,5) and (6,9), we can substitute the values into the slope formula:
m = (9 - 5) / (6 - 4)
m = 4 / 2
m = 2
Therefore, the slope (m) of the line is 2.
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can substitute the coordinates of one of the given points into the equation y = mx + b and solve for b.
Let's use the point (4,5):
5 = 2(4) + b
5 = 8 + b
b = 5 - 8
b = -3
Therefore, the y-intercept (b) of the line is -3.
Step 3: Write the equation
Now that we have both the slope (m) and the y-intercept (b), we can write the equation for the line:
y = 2x - 3
Hence, the equation of the line passing through the points (4,5) and (6,9) is y = 2x - 3.