Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
Line j passes through points (8, 10) and (4, 1). Line k is parallel to line j. What is the slope of line k?
To find the value of b in the slope-intercept form, y = mx + b, we need to first find the slope (m) of the line.
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given points J(–4, –5) and K(–6, 3), we can substitute the coordinates into the formula:
m = (3 - (-5)) / (-6 - (-4))
m = (3 + 5) / (-6 + 4)
m = 8 / (-2)
m = -4
Now that we have the slope (m) of -4, we can write the equation of the line in slope-intercept form:
y = mx + b
Substituting the slope (-4) and the coordinates of one of the points (J or K), let's use point J(–4, –5):
-5 = -4(-4) + b
-5 = 16 + b
To find b, we can solve the equation:
-5 - 16 = b
-21 = b
Therefore, the value of b is -21.
To find the value of b in the slope-intercept form y = mx + b, we need to express the equation of the line in terms of its slope (m) and the y-intercept (b).
The slope (m) can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of any two points on the line.
In this case, we can use the coordinates of points J(-4, -5) and K(-6, 3) to find the slope:
m = (3 - (-5)) / (-6 - (-4))
m = (3 + 5) / (-6 + 4)
m = 8 / -2
m = -4
Now that we have the slope (m), we can substitute it into the slope-intercept form to find the equation of the line:
y = mx + b
Using point J(-4, -5):
-5 = -4*(-4) + b
-5 = 16 + b
b = -21
Therefore, the value of b is -21.
slope JK = (3+5)/(-6+4) = 8/-2 = -4
so you have
y = -4x + b
plug in either point and solve for b
What did you get ?