find an equation for the line with the given properties. express the equation in slope-intercept form containing the points.
P=(-5,4) and Q=(-4,2)
plz show work
To find the equation for the line passing through two given points, we can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope of the line, and b represents the y-intercept.
Step 1: Calculate the slope (m)
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let's substitute the values into the formula:
m = (2 - 4) / (-4 - (-5))
m = (-2) / (-4 + 5)
m = (-2) / (1)
m = -2
Step 2: Determine the y-intercept (b)
We can determine the y-intercept (b) by substituting the x and y values from one of the given points into the slope-intercept form equation (y = mx + b) and solving for b.
Let's use point P(-5, 4):
4 = -2(-5) + b
4 = 10 + b
b = 4 - 10
b = -6
Step 3: Write the equation in slope-intercept form
Now that we have the values of m (-2) and b (-6), we can write the equation in slope-intercept form (y = mx + b) using any of the given points.
Let's use point P(-5, 4):
y = -2x - 6
Therefore, the equation for the line passing through points P(-5, 4) and Q(-4, 2) in slope-intercept form is y = -2x - 6.