Respuesta :
The slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is [tex]y=-\frac{9}{8}x+\frac{11}{4}[/tex]
We know that the slope-intercept form of the line is y = mx + c, where m is the slope of the line and c is the y-intercept of the line.
For given question we have been given two points (-2,5) and (6,-4)
We need to find the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4).
Using two-point form the equation of the line is,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]
Let (x1, y1) = (-2,5) and (x2, y2) = (6,-4)
So, the equation of the line is,
[tex]\frac{y-5}{-4-5} =\frac{x-(-2)}{6-(-2)}\\\\ \frac{y-5}{-9} =\frac{x+2}{6+2}\\\\\frac{y-5}{-9} =\frac{x+2}{8}\\\\ 8(y-5)=-9(x+2)\\\\8y-40=-9x-18\\\\8y=-9x-18+40\\\\8y=-9x+22\\\\y=-\frac{9}{8}x+\frac{11}{4}[/tex]
above equation is in the slope-intercept form.
Therefore, the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is [tex]y=-\frac{9}{8}x+\frac{11}{4}[/tex]
Learn more about the slope-intercept equation of a line here:
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