Write the standard form of the equation of the line through the given point with the given slope. Through: (3,-1) and (8,-4)
Slope = (-4 - (-1))/(8-3) = -3/5
using the point (3,-1)
y+1 = (-3/5)(x-3)
5y + 5 = -3x + 9
3x + 5y = 4
Test my subbing in the point not used, it works.
To find the standard form of the equation of a line, we need to use the point-slope form first and then rearrange the equation into standard form.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Given the points (3, -1) and (8, -4), we can find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (-4 - (-1)) / (8 - 3)
m = (-4 + 1) / (8 - 3)
m = -3 / 5
Now, we have the slope (m) and the point (3, -1). We can substitute these values into the point-slope form equation:
y - (-1) = (-3/5)(x - 3)
Simplifying the equation:
y + 1 = (-3/5)(x - 3)
Now, let's convert this equation into the standard form, which is Ax + By = C.
To do this, we need to clear the parentheses and rearrange the terms:
y + 1 = (-3/5)(x - 3)
y + 1 = (-3/5)x + (9/5)
Multiply all the terms by 5 to get rid of the fraction:
5y + 5 = -3x + 9
Rearrange the terms to get the standard form:
3x + 5y = 4
Therefore, the standard form of the equation of the line passing through the points (3,-1) and (8,-4) is:
3x + 5y = 4.