Write an equation of a line that passes through the two given points. Your answer should be written in slope-intercept form.
P(6, 0), Q(7, −5)
y = -5 x + 30
To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
Where:
- y is the dependent variable (the value we are trying to find)
- x is the independent variable (the given variable)
- m represents the slope of the line
- b is the y-intercept (the point where the line crosses the y-axis)
To determine the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given points P(6, 0) and Q(7, −5):
m = (-5 - 0) / (7 - 6)
m = -5 / 1
m = -5
Now that we have the slope, we can substitute it into the slope-intercept form, along with one of the given points (let's use point P):
0 = -5(6) + b
Next, we can solve for b:
0 = -30 + b
b = 30
Now we have the slope (m = -5) and the y-intercept (b = 30). Plugging these values into the equation, the final equation for the line passing through points P(6, 0) and Q(7, −5) is:
y = -5x + 30