line k has a slope of -5 line j is perpendicular to line k and passes through the point (5, 9) create the equation for line j
Since line j is perpendicular to line k, the slope of line j will be the negative reciprocal of the slope of line k. The negative reciprocal of -5 is 1/5.
We know that line j passes through the point (5, 9). We can use the point-slope form of a linear equation to write the equation of line j.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Substituting the given values, we get:
y - 9 = (1/5)(x - 5)
Simplifying the equation gives us the final equation for line j:
y - 9 = (1/5)x - 1
Rearranging the equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we have:
y = (1/5)x + 8
what is the formula
The formula to find the equation of a line is the point-slope form:
y - y₁ = m(x - x₁)
Where:
- (x₁, y₁) is a point on the line
- m is the slope of the line
By substituting the given values into this formula, we can find the equation for line j.
To find the equation of a line, we need to use the slope-intercept form:
y = mx + b
We already know that line k has a slope of -5. The slopes of perpendicular lines are negative reciprocals of each other. So, for line j, the slope will be the negative reciprocal of -5, which is 1/5.
We also know that line j passes through the point (5, 9). We can substitute these values into the equation and solve for the y-intercept (b).
9 = (1/5) * 5 + b
9 = 1 + b
b = 9 - 1
b = 8
Now that we have the slope (m = 1/5) and the y-intercept (b = 8), we can write the equation for line j:
y = (1/5)x + 8
Thus, the equation for line j is y = (1/5)x + 8.