Which equation represents the line that passes through the points (4,10) and (2,7)?
What are your choices?
Lol
To find the equation of a line that passes through two given points, we can use the slope-intercept form of a linear equation, which is:
𝑦 = 𝑚𝑥 + 𝑏
where 𝑦 is the dependent variable (usually representing the vertical axis), 𝑚 is the slope of the line, 𝑥 is the independent variable (usually representing the horizontal axis), and 𝑏 is the y-intercept.
To find the slope (𝑚), we can use the formula:
𝑚 = (𝑦₂ - 𝑦₁) / (𝑥₂ - 𝑥₁)
where (𝑥₁, 𝑦₁) and (𝑥₂, 𝑦₂) are the coordinates of the given points.
Using the points (4, 10) and (2, 7), we can substitute the values into the slope formula:
𝑚 = (7 - 10) / (2 - 4)
Simplifying further, we get:
𝑚 = -3 / -2
𝑚 = 3/2
Now that we have the slope (𝑚), we can substitute it along with the coordinates of one point (let's use (2, 7)) into the slope-intercept form equation:
𝑦 = 𝑚𝑥 + 𝑏
7 = (3/2)(2) + 𝑏
Simplifying further:
7 = 3 + 𝑏
Subtracting 3 from both sides:
4 = 𝑏
Now we have the slope (𝑚 = 3/2) and the y-intercept (𝑏 = 4), so we can write the equation of the line:
𝑦 = (3/2)𝑥 + 4
Hence, the equation representing the line passing through the points (4,10) and (2,7) is 𝑦 = (3/2)𝑥 + 4.
the slope is (7-10)/(2-4) = 3/2
The point-slope form yields
y-10 = 3/2 (x-4)