Answer :
The equation of the line in slope intercept form is y = [tex]13x + 19[/tex]
Given that,
In math, slope intercept form is a way of writing an equation for a line in the form y = mx + b. The m represents the slope of the line and the b represents the y-intercept. The slope intercept form is used when you want to find either a point on a line or solve for y if you know x.
We have,
The line that passes through ( -2, -7) and ( -1, 6)
[tex]x_{1} =-2\\y_{1} =-7\\x_{2} =-1\\y_{2} =6[/tex]
We know that the formula to find the slope of two points (x1, y1) and (x2, y2) is:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m = [tex]\frac{6-(-7)}{-1-(-2)}[/tex]
m = [tex]\frac{6+7}{-1+2}[/tex]
m = [tex]\frac{13}{1}[/tex]
m = 13
Now using the slope and the point (-2, -7) the y-intercept is
y = mx + b
-7 = 13 (-2) + b
-7 = -26 + b
b = -7 + 26
b = 19
We can substitute the b value in y = mx + b expression,
So,
We can write,
y = mx + b
y = [tex]13x + 19[/tex]
Therefore,
The equation of the line in slope intercept form is y = [tex]13x + 19[/tex]
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