Find the equation of the line that passes through (-2,5) and (-6,-3).
To find the equation of a line, you will need to use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where:
- m is the slope of the line
- x and y are the coordinates of a point on the line
- b is the y-intercept, the point where the line intersects the y-axis
To find the slope (m) of the line, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where:
- (x1, y1) and (x2, y2) are the coordinates of two points on the line
Let's use the points (-2,5) and (-6,-3) to find the slope of the line:
m = (-3 - 5) / (-6 - (-2))
= (-3 - 5) / (-6 + 2)
= (-8) / (-4)
= 2
Now that you have the slope (m = 2), you can substitute it into the slope-intercept form (y = mx + b) along with the coordinates of one of the points to find the y-intercept (b).
Using the point (-2,5):
5 = 2(-2) + b
5 = -4 + b
b = 5 + 4
b = 9
Now we have the slope (m = 2) and the y-intercept (b = 9), so we can write the equation of the line:
y = 2x + 9
Therefore, the equation of the line that passes through (-2,5) and (-6,-3) is y = 2x + 9.