How do you write an equation of a line given point (1,3) and m=-3/4?

Question

Isaiah Anthony · Accepted Answer

Use the point-slope formula to write the equation of the line. See the full explanation below:

Use the point-slope formula to write the equation of the line.

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the point and the slope from the problem gives the result:

#(y - color(red)(3)) = color(blue)(-3/4)(x - color(red)(1))#

We can convert this to the more familiar slope=intercept form by solving for #y#:

#y - color(red)(3) = color(blue)(-3/4)x - (color(blue)(-3/4) xx color(red)(1))#

#y - color(red)(3) = color(blue)(-3/4)x + 3/4#

#y - color(red)(3) + 3 = color(blue)(-3/4)x + 3/4 + 3#

#y - 0 = color(blue)(-3/4)x + 3/4 + (4/4 xx 3)#

#y = color(blue)(-3/4)x + 3/4 + 12/4#

#y = -3/4x + 15/4#

Ethan Adkins · Answer

undefined To write the equation of a line given a point (1,3) and slope $ m = -\frac{3}{4} $, you can use the point-slope form of a linear equation:

$$ y - y_1 = m(x - x_1) $$

where $ (x_1, y_1) $ represents the given point, and $ m $ is the slope.

Substitute the values into the equation:

$$ y - 3 = -\frac{3}{4}(x - 1) $$

Simplify:

$$ y - 3 = -\frac{3}{4}x + \frac{3}{4} $$

Add 3 to both sides to isolate $ y $:

$$ y = -\frac{3}{4}x + \frac{3}{4} + 3 $$

$$ y = -\frac{3}{4}x + \frac{3}{4} + \frac{12}{4} $$

$$ y = -\frac{3}{4}x + \frac{15}{4} $$

Therefore, the equation of the line is $ y = -\frac{3}{4}x + \frac{15}{4} $.