Question

What is the equation for a line that passes through the points (5,-4) and (-10,17

Answer 1

The equation of line passing through (5,-4) and (-10,17) is:

$y = -\frac{7}{5}x+3$

Step-by-step explanation:

Given points are:

(x1,y1) = (5,-4)

(x2,y2) = (-10,17)

The equation of line in slope-intercept form is given by:

$y = mx+b$

First of all, we have to find the slope of the line

Slope is given by:

$m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{17-(-4)}{-10-5}\\m = \frac{17+4}{-15}\\m = \frac{21}{-15}\\m = -\frac{7}{5}$

Putting the value of slope in the equation

$y = -\frac{7}{5}x+b$

To find the value of b, putting (5,-4) in equation

$-4 = -\frac{7}{5}(5) + b\\-4 = -7 +b\\b = 7-4\\b = 3$

Putting the value of b:

$y = -\frac{7}{5}x+3$

Hence,

The equation of line passing through (5,-4) and (-10,17) is:

$y = -\frac{7}{5}x+3$

Keywords: Equation of line, slope

Learn more about equation of line at:

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