The equation of line passing through (5,-4) and (-10,17) is:
[tex]y = -\frac{7}{5}x+3[/tex]
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:
[tex]y = mx+b[/tex]
First of all, we have to find the slope of the line
Slope is given by:
[tex]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}[/tex]
Putting the value of slope in the equation
[tex]y = -\frac{7}{5}x+b[/tex]
To find the value of b, putting (5,-4) in equation
[tex]-4 = -\frac{7}{5}(5) + b\\-4 = -7 +b\\b = 7-4\\b = 3[/tex]
Putting the value of b:
[tex]y = -\frac{7}{5}x+3[/tex]
Hence,
The equation of line passing through (5,-4) and (-10,17) is:
[tex]y = -\frac{7}{5}x+3[/tex]
Keywords: Equation of line, slope
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