Which is the equation of the line that contains the points (0,3) and (-2,4)?
slope = (4-3)/(-2-0) = -1/2
since (0,3) is the y-intercept
y = (-1/2)x + 3 ...... all done
To find the equation of a line that passes through two given points, you can use the point-slope formula. The point-slope formula is given by:
(y - y₁) = m(x - x₁),
where (x₁, y₁) represents one point on the line, and m represents the slope of the line.
Step 1: Determine the slope of the line
The slope (m) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁),
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two given points.
Using the given points (0,3) and (-2,4), we can substitute these values into the formula to find the slope:
m = (4 - 3) / (-2 - 0)
= 1 / -2
= -1/2.
Step 2: Choose one of the points and substitute its coordinates
You can choose either point to substitute into the point-slope formula. Let's choose (0,3) as our point.
Using the point-slope formula, we have:
(y - 3) = (-1/2)(x - 0).
Step 3: Simplify the equation
Distribute the -1/2 to the x term:
y - 3 = (-1/2)x.
Step 4: Rewrite the equation in slope-intercept form
To get the equation in slope-intercept form (y = mx + b), isolate the y variable:
y = (-1/2)x + 3.
Therefore, the equation of the line passing through the points (0,3) and (-2,4) is y = (-1/2)x + 3.
To find the equation of a line that passes through two given points, you can use the point-slope form of a linear equation.
The point-slope form is represented as y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.
Let's use the points (0, 3) and (-2, 4).
First, we need to find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values, we get:
m = (4 - 3) / (-2 - 0)
m = 1 / -2
m = -1/2
Now we have the slope (m = -1/2). We can choose either point (0, 3) or (-2, 4) to substitute into the point-slope form.
I'll choose (0, 3):
y - 3 = (-1/2)(x - 0)
Simplifying, we get:
y - 3 = (-1/2)x
To write the equation in slope-intercept form (y = mx + b), we can rearrange the equation:
y = (-1/2)x + 3
Therefore, the equation of the line that contains the points (0, 3) and (-2, 4) is y = (-1/2)x + 3.