Indicate the equation of the line through (2, -4) and having slope of 3/5.
y = (3/5)x + b
plug in the given point ...
-4 = (3/5)(2) + b
b = -26/5
y = (3/5)x - 26/5
To find the equation of the line through a given point and with a given slope, you can use the point-slope form of a linear equation. The point-slope form is:
y - y1 = m(x - x1)
Where (x1, y1) are the coordinates of the given point, and m is the slope of the line.
In this case, the given point is (2, -4), and the slope is 3/5. Plugging these values into the point-slope form, we get:
y - (-4) = (3/5)(x - 2)
Simplifying the equation further:
y + 4 = (3/5)(x - 2)
Expanding the equation:
y + 4 = (3/5)x - (3/5)(2)
y + 4 = (3/5)x - 6/5
To isolate y, subtract 4 from both sides of the equation:
y = (3/5)x - 6/5 - 4
y = (3/5)x - 6/5 - 20/5
Combining the terms on the right side:
y = (3/5)x - 26/5
Therefore, the equation of the line that passes through the point (2, -4) and has a slope of 3/5 is y = (3/5)x - 26/5.