find the y-intercept of a line that passes through (2,1) and has a slope of -5.
i forgot what equation i have to use to find this out. can someone give me which equation i have to use?
or all the equations that deal with slopes please
A line of slope m passing through the point P1(x1,y1) has the equation:
(y-y1)=m(x-x1)
Post your answer if you need a check.
But you can check your own answer by substituting (x1,y1) in the equation to see if the two sides balance.
Oh yes, the y-intercept can be found by setting x=0 in the resulting equation of the line.
If you simplify the equation of the line using x=0, you should get:
y-intercept = y1-mx1
To find the y-intercept of a line that passes through a given point and has a known slope, you can use the point-slope form of the equation for a line. The equation is:
y - y₁ = m(x - x₁)
In this equation, (x₁, y₁) represents the coordinates of the given point, and m is the slope of the line. By rearranging this equation, you can determine the y-intercept.
Let's solve the problem step by step using the equation.
Given:
Point (x₁, y₁) = (2, 1)
Slope (m) = -5
Step 1: Substitute the values into the point-slope form equation:
y - 1 = -5(x - 2)
Step 2: Simplify the equation:
y - 1 = -5x + 10
Step 3: Move the constant term to the opposite side of the equation:
y = -5x + 10 + 1
y = -5x + 11
Step 4: Now we have the equation of the line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept (b) is 11.
Therefore, the y-intercept of the line that passes through (2,1) with a slope of -5 is 11.