Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form.
P(−2, 1); m = 1
since you have a point and a slope, start with the point-slope form. That way you don;t have to solve for m and b.
y-1 = 1(x+2)
y = x+3
Why did the line go to the therapist? It had trouble expressing itself in slope-intercept form! But don't worry, I'm here to help.
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.
Given the point P(-2, 1) and the slope m = 1, we can substitute these values into the slope-intercept form:
1 = 1*(-2) + b
Simplifying, we get:
1 = -2 + b
To find b, we add 2 to both sides:
1 + 2 = b
b = 3
Now we can write the equation in slope-intercept form:
y = 1x + 3
Finally, let's convert the equation to standard form, Ax + By = C:
y - 1 = 1x + 3
Rearranging, we get:
x - y = -4
So, the equation of the line passing through the point P(-2, 1) with a slope of 1 in standard form is x - y = -4. Keep up the good work in math!
To write an equation of a line using slope-intercept form, we need two pieces of information: the slope (m) and a point on the line (x, y). In this case, the slope (m) is 1, and the point on the line is P(-2, 1).
Slope-intercept form: y = mx + b
Step 1: Substitute the given slope (m) into the equation:
y = 1x + b
Step 2: Plug in the coordinates of the given point (-2, 1) to find the value of b:
1 = 1*(-2) + b
Simplifying the equation:
1 = -2 + b
Step 3: Solve for b:
1 + 2 = b
3 = b
Step 4: Substitute the value of b (3) back into the equation:
y = x + 3
To express the equation in standard form, we'll rearrange the equation by moving the x term to the left side of the equation:
y - x = 3
Therefore, the equation of the line, in standard form, passing through the point (-2, 1) with slope m = 1 is y - x = 3.
To write the equation of a line using slope-intercept form, we use the equation:
y = mx + b
Where:
- y is the dependent variable (typically representing the y-coordinate of a point on the line)
- x is the independent variable (typically representing the x-coordinate of a point on the line)
- m is the slope of the line
- b is the y-intercept (the point where the line intersects the y-axis)
In this case, we are given the point P(-2, 1) and the slope m = 1.
Step 1: Substitute the slope value into the equation.
y = 1x + b
Step 2: Substitute the coordinates of the given point (-2, 1) into the equation to find the value of b.
1 = 1(-2) + b
1 = -2 + b
1 + 2 = b
b = 3
Step 3: Substitute the found values of m and b back into the equation.
y = 1x + 3
The equation of the line passing through the point P(-2, 1) with a slope of 1 is y = x + 3.
To express the equation in standard form, we need to rearrange the equation to have the form Ax + By = C, where A, B, and C are integers and A is positive.
In this case, the equation y = x + 3 can be rearranged as:
x - y = -3
So, the equation of the line in standard form is x - y = -3.