The first step of writing an equation when given two points is the same for both strategies, slope-intercept or point-slope forms. What would be the first step in finding the equation of the line that passes through (5, 1) and (3, 5)?
create a graph using the two points
find the slope
find the y-intercept
substitute one point’s coordinates into either form
find the slope
Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, to find the slope of a line that passes through the points (–3, 8) and (4, –6).
m =
Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.
b =
What is the new equation written in slope-intercept form, y = mx + b?
m = (8 - (-6))/( -3 - 4) = -2
b = y - mx = 8 - (-2)*(-3) = 2
The equation in slope-intercept form is y = -2x + 2.
Use slope-intercept form, y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).
y = –3x + 5
y = 3x – 5
y = one-third x + 3
y = negative one-third x + 5
First, we need to find the slope:
m = (4 - 1) / (3 - (-6)) = 3/9 = 1/3
Next, we need to find the y-intercept (b) by substituting one of the points and the slope into the slope-intercept form:
1 = (1/3)(-6) + b
b = 3
Therefore, the equation of the line is y = (1/3)x + 3. Answer: y = one-third x + 3.
Which statements are correct steps in finding the linear equation of a line that passes through the points (−1, 7) and (2, 4) using the point-slope form method? Select all that apply.
y = x + 6
7 = –1(–1) + b
y – 4 = –1 (x – 2)
y – 7 = –1 (x – (–1))
y – 2 = x – 4
y = –x + 6
Some correct steps in finding the linear equation of a line that passes through the points (−1, 7) and (2, 4) using the point-slope form method are:
- Choose one of the given points to be the point (x1, y1) in the point-slope form.
- Find the slope of the line by using the slope formula with the two given points.
- Substitute the slope and the point (x1, y1) into the point-slope form and simplify.
So the correct statements are:
- 7 = –1(–1) + b
- y - 4 = -1(x - 2)
- y - 7 = -1(x - (-1))