Choose 1 set of points from the choices below. Then, solve the problem and post your solution, showing your steps.
Write an equation in point-slope form for the line that passes through one of the following pairs of points (you may choose the pair you want to work with). Then, use the same set of points to write the equation in standard form and again in slope-intercept form.
Point pairs
(5, 1), (–3, 4)
(0, –2), (3, 2)
(–2, –1), (1, 2)
I chose the last one. For slope-intercept form, I have y = 1x + 1. For point-slope form, I have y + 1 = 1(x + 2). For standard form, I have 1x - y = -1.
Could you please check if my answers are correct?
looks good to me, though why you bother with the 1x notation is unclear.
To check if your answers are correct, we will derive the equation in point-slope form, standard form, and slope-intercept form using the given set of points (–2, –1) and (1, 2):
1. Point-Slope Form:
The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where (x1, y1) represents one of the given points and m is the slope of the line.
Using the formula, we substitute the values (x1, y1) = (–2, –1) and the slope m = (change in y) / (change in x) = (2 - (-1)) / (1 - (-2)) = 3/3 = 1:
y - (-1) = 1(x - (-2))
y + 1 = x + 2
Therefore, the equation in point-slope form is: y + 1 = x + 2.
2. Standard Form:
The standard form of a linear equation is given by: Ax + By = C, where A, B, and C are constants.
To convert the equation from point-slope form to standard form, we will rearrange the terms:
y + 1 = x + 2
x - y = 2 - 1
x - y = 1
So, the equation in standard form is: x - y = 1.
3. Slope-Intercept Form:
The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.
To convert the equation from point-slope form to slope-intercept form, we will solve for y:
y + 1 = x + 2
y = x + 2 - 1
y = x + 1
Therefore, the equation in slope-intercept form is: y = x + 1.
Your results are correct for the given set of points (–2, –1) and (1, 2). Well done!